Market Finder by Google


Thinking about expanding your business abroad? Google’s free Market Finder tool can help you get going. Just start by telling us a bit about your busines and we’ll recommend the most valuable export markets for you based on your goals. You’ll also discover key insights about each one Like how much people earn on average, how often they go online, or even how many monthly searches there are for your product or service. Plus you can get advice from real experts on everything from taking payments and localising your marketing to hiring the right people and navigating tax and legal laws. Market Finder can also help you create a global marketing strategy For example, with tips on how to take your website global helping international customers find you online and measuring your success. Find new customers abroad and take your business further with Market Finder.

2019 Growth, Enterprise, Employment and Livelihoods (GEEL) in Somaliland


(GEEL IN SOMALILAND) The GEEL project promotes inclusive economic growth in Somaliland in the fish, livestock, and agriculture sectors. (Mohammed Yusef, Hargeisa Office Manager) The name of the project, GEEL stands for Growth, Enterprise, Employment, and Livelihoods. The project works with high-potential businesses in the fish, livestock, and agriculture sectors. GEEL also works closely with the government ministries and institutions to integrate Somaliland into the global economy through networking and investment facilitation. We introduced renewable energy technologies like solar to businesses in the fish and agriculture sectors and this has substantially reduced their dependency on the expensive nonrenewable energy sources. (Mustafa Sa’ad, Chairman Horn Gardens) Horn Gardens Company was founded in 2016 and is co-owned by a number of Somlilanders. In the two years we have been operating, we have partnered with the GEEL project. Their assistance made it possible for us to establish a one-stop shop where the farmers could buy everything they need including seeds, fertilizer, and pesticides. We have also managed to bring smart farming techniques, such as drip irrigation and greenhouse cultivation to many people and places. (Abdulrahman Ibrahim, Production Manager Somaliland Beverages Industry) The GEEL project worked with us at Lis Dairies in 2017 and 2018. They provided trainings to Lis factory employees. The trainings started hygiene and sanitation, because milk production is more sensitive than other beverages. Employees learned to observe appropriate hygiene, from uniforms to washing hands before stepping into the factory, and that the factory must be clean and sanitary at all times. The next trainings for operators were about the production process, so that they could ensure international standards and a high quality of milk and other juices produced. The importance of this workshop is to bring together electricity sector stakeholders, especially those that work with the electrical power and on distribution lines This conference led by the Ministry of Energy and Minerals, brought together the electric companies, international organizations and consumers. (Rahma Mohamed, Energy Intern) I am a graduating student at the University of Hargiesa’s Faculty of Engineering and Electronic Engineering. GEEL has assisted us with many things including giving us several trainings. This trainings included how to design and maintain solar energy systems. In addition, GEEL facilitated internships for us. so that we could practically see and demonstrate what they have taught us. The GEEL project works with us to access markets for our fish. They also assist us with cold storage of the fish. GEEL staff conducted trainings on how to improve and maintain fish quality standards. Everything is going great for us This project is really encouraging, and we appreciate it very much. (USAID impact in Somaliland to date:$650, 800 Export sales by GEEL partners; 336 Full-time equivalent jobs created; $2,935,106 New private capital investment)

What is market research?


Did you know that one of the main reasons
would-be entrepreneurs fail is because they haven’t done their market research. It’s easy for you to believe you have an excellent
idea for a business! But if you want your business to be a success, it’s a good idea
to check it out more widely. Is there really a market for your business and will people
actually buy your products or services? That’s what market research is – a cost-effective
way to check out if your idea is a winner. Market research provides you with answers
and information so that you can make better decisions. You can find out what your customers
want and then match your products and services so that they ‘fit’ better. It can make you
more competitive and improve your chances of success. You don’t always get NEW information from
your market research. Sometimes it confirms what you already know – but you have wider
proof, so it’s not just your opinion or that of your family and friends. And make sure
you take notice of what you learn – there may be small but important facts hidden in
your research that make all the difference to your success. Of course, it’s not always completely positive.
Market research can throw up results that are critical or negative. That can be tough
to take, but don’t hide away or ignore it. Some of those comments may be well founded.
They may give you valuable insights so that you can refine or adapt what you are offering,
or make changes to your pricing. You may even get some hints and tips on how to do your
marketing better. You may be thinking that this sounds great,
but hiring a market research professional is expensive. But don’t worry. There are lots
of simple and low-cost techniques that you can use to get the information you need. There’s
more about these in this module – have a look and you’ll be well equipped to do-it-yourself. But remember, market research doesn’t make
decisions for you – and of course, there’s no guarantee of success. Market research is crucial during the start-up
phase of your business. And it’s equally important once you’re established. You still need to
know about your market, your competitors and your customers. Tastes and trends change all
the time and it’s easy to get left behind. After all, a beautician who isn’t up-to-date
with the latest treatments will soon lose out! And an interior designer who is offering
last year’s colours isn’t likely to do too well either! Use the information in this module to find
out how market research can help you make informed decisions and improve your chances
of success.

How to Decide The Best Occupation As Per Astrology?


Are you understanding? One soldier could be belong to a good Mars, One soldier could be belong to a good Mars, but a care taker cannot belong to a Mars. Any work regarding force, any work in which action is required. The one who work for ambulance he must instant required, at the same moment, so in that person, the involvement of Mangal will be there. Now if you ask the person to join a army, who is care taking, then he will say no, I cannot, if I will hit then blood will come. Are you understanding? The person’s nature, the qualities when
he born. It is in his escended Lord or the sights on him, that shape up the person. When situation of planets forms in the universe, at that time you born which means you need to go in a state and your formation, your thinking will be like this, now it does not mean that you are wander form the things that is why you are in the pain. You have the qualities inside you naturally, at that time the placements of stars, which is inside you. Brahspati’s person fits in the kark Raashi. Jupiter & Moon, have you heard about Ghaj Kesari Yog. There must be a Guru and Love must be in him or it make in the Kendra, it has combinations forms in the Kendra, or it sits together and makes Ghaj Kesari Yog. So there must be love in the Guru Ji, and that Ghaj Kesari Yog. Actually this is the definition of Yoga. It takes a person on heights, and if you ask a Guru element person to join the Army, he will say No, I cannot because it is Sin. To hit someone is a Sin. A person belongs to water element will be emotional, if I will hit this person he will feel pain, one wrestler or a fighter never belongs to water element which means Kark Raashi, Kark Raashi means related to Moon. That Person will belong to Mangal, belongs to Force.

HubSpot Marketing Starter 🏆 (2019) Pricing HubSpot Marketing Starter


HubSpot Marketing Starter 2019 – Pricing HubSpot Marketing Starter so now looking at HubSpot let’s take a
look at their marketing option here it’s called the marketing hub what you can
see here is something right off the bat which is there is a low barrier to entry
they do have a free option of course as you click through these you can see just
as with par dot that you have not every feature in the lower plans but as you
move up you begin to get all of those great benefits and features well what I
would point out to you here is that there is tremendous benefit in having
the marketing automation piece which is available at a lower price here you can
see so mom-and-pop shops or small types of businesses can get into this at a
lower threshold even the enterprise product substantially lower then part
out here at $2,400 a month this has all the bells and whistles as you can see
it’s also important to note is that HubSpot is tops in the industry seeing
numerous reviews on them on review sites and they are at the top they are well
liked I’ve used par dot and hub spot so I can tell you from my own personal
experience both nice tools to have at your fingertips and so what it really
comes down to is does it meet your threshold for your budget and is it
something that you can grow into and feel things out at first without putting
down a whole lot of money in here of course you’ve got that option with
HubSpot with all of these other types of options where you can grow into the
product if you so need to even at the professional level you do have marketing
automation available to you right here so to get some more of those triggering
options and more advanced types of things we’d have to go up to enterprise
but still nice to know that just for eight hundred bucks a month with the
contacts not being an issue both products pretty much have the same
charge for additional contacts and all of these are slated at 10,000 contacts
starting out so these are the key things most people are going to be looking for
when they’re looking for an automation product
one final thing I’d mention while we’re in here is notice that HubSpot has
everything together nice and neat all in one type of location you have the
HubSpot CRM which is critical for any marketing automation platform to work
along with the CRM and here you’ll notice something pretty spectacular it
is free forever as they have it listed so it’s been this way for a few years
that I’ve monitored it and it is still free forever so it appears that it’s
going to be free forever and I can tell you it’s very easy to work with in the
CRM and it’s important to have the CRM to leverage your marketing automation
platforms so definitely a very big factor when choosing a marketing
automation platform here you’ve got the free CRM something definitely to
consider also these lower barrier to entry pricing tiers for the other tools
regarding your sales team as they work along with your marketing team you so now looking at HubSpot let’s take a
look at their marketing option here it’s called the marketing hub what you can
see here is something right off the bat which is there is a low barrier to entry
they do have a free option of course as you click through these you can see just
as with par dot that you have not every feature in the lower plans but as you
move up you begin to get all of those great benefits and features well what I
would point out to you here is that there is tremendous benefit in having
the marketing automation piece which is available at a lower price here you can
see so mom-and-pop shops or small types of businesses can get into this at a
lower threshold even the enterprise product substantially lower than part
out here at $2,400 a month this has all the bells and whistles as you can see
what’s also important to note is that HubSpot is tops in the industry seeing
numerous reviews on them on review sites and they are at the top they are well
liked I’ve used par dot and hub spot so I can tell you from my own personal
experience both nice tools to have at HubSpot Marketing Starter 2019 – Pricing HubSpot Marketing Starter your fingertips and so what it really
comes down to is does it meet your threshold for your budget and is it
something that you can grow into and feel things out at first without putting
down a whole lot of money in here of course you’ve got that option with
HubSpot with all of these other types of options where you can grow into the
product if you so need to even at the professional level you do have marketing
automation available to you right here so to get some more of those triggering
options and more advanced types of things we’d have to go up to enterprise
but still nice to know that just for 800 bucks a month
with the context not being an issue both products pretty much have the same
charge for additional contacts and all of these are slated at 10,000 contacts
starting out so these are the key things most people are going to be looking for
when they’re looking for an automation product
one final thing I’d mention while we’re in here is notice that HubSpot has
everything together nice and neat all in one type of location you have the
HubSpot CRM which is critical for any marketing automation platform to work
along with the CRM and here you’ll notice something pretty spectacular it
is free forever as they have it listed so it’s been this
way for a few years that I’ve monitored it and it is still free forever so it
appears that it’s going to be free forever and I can tell you it’s very
easy to work with in the CRM and it’s important to have the CRM to leverage
your marketing automation platforms so definitely a very big factor when
choosing a marketing automation platform here you’ve got the free CRM something
definitely to consider also these lower barrier to entry pricing tiers for the
other tools regarding your sales team as they work along with your marketing team so now looking at HubSpot let’s take a
look at their marketing option here it’s called the marketing hub what you can
see here is something right off the bat which is there is a low barrier to entry
they do have a free option of course as you click through these you can see just
as with par dot that you have not every feature in the lower plans but as you
move up you begin to get all of those great benefits and features well what I
would point out to you here is that there is tremendous benefit in having
the marketing automation piece which is available at a lower price here you can
see so mom-and-pop shops or small types of businesses can get into this at a
lower threshold even the enterprise product substantially lower then part
out here at $2,400 a month this has all the bells and whistles as you can see
but it’s also important to note is that HubSpot is tops in the industry seeing
numerous reviews on them on review sites and they are at the top they are well
liked I’ve used par dot and hub spot so I can tell you from my own personal
experience both nice tools to have at your fingertips and so what it really
comes down to is does it meet your threshold for your budget and is it
something that you can grow into and feel things out at first without putting
down a whole lot of money in here of course you’ve got that option with
HubSpot with all of these other types of options where you can grow into the
product if you so need to even at the professional level you do have marketing
automation available to you right here so to get some more of those triggering
options and more advanced types of things we’d have to go up to enterprise
but still nice to know that just for 800 bucks a month
with the contacts not being an issue both products pretty much have the same
charge for additional contacts and all of these are slated at 10,000 contacts
starting out so these are the key things most people are going to be looking for
when they’re looking for an automation product
one final thing I’d mentioned while we’re in here is notice that HubSpot has
everything together nice and meet all in one type of location you have the
HubSpot CRM which is critical for any HubSpot Marketing Starter 2019 – Pricing HubSpot Marketing Starter marketing automation platform to work
along with the CRM and here you’ll notice something pretty spectacular it
is free forever as they have it listed so it’s been this way for a few years
that I’ve monitored it and it is still free forever so it appears that it’s
going to be free forever and I can tell you it’s very easy to work with in the
CRM and it’s important to have the CRM to leverage your marketing automation
platforms so definitely a very big factor when choosing a marketing
automation platform here you’ve got the free CRM something definitely to
consider also these lower barrier to entry pricing tiers for the other tools
regarding your sales team as they work along with your marketing team

Moody’s forecasts S. Korea’s economic growth for 2020 at 2.1%


Moody’s forecast South Korea’s economy
to grow at a relatively weak 2.1 percent next year it’s also passed mystic about
local companies the credit ratings agency believes export-dependent firms
are seeing weaker profitability due to trade disputes especially so for
industries that are in a down cycle like semiconductors and chemicals Moody’s
gave negative outlooks to 14 out of 24 related companies Trias sovereign credit
rating however will say at the second highest level of double-a

Growth Stock Portfolio 2020 – Building a Growth Portfolio for the Long Run


Hi I’m Jimmy in this video we’re looking at the growth stocks that are gonna make up our growth portfolio from our Dow 30 analysis. Now if you’re new to this channel Well we’ve been doing an analysis that we’re calling the Dow 30 analysis where we analyze all 30 companies in the Dow Jones industrial average. We then take that analysis. We’re building three different portfolios a value a dividend and a growth portfolio. This is a growth portfolio. We already did the value in the dividend portfolio. So my goal here is to pick companies that are growing relatively quickly or they’re growing we expect them to grow relatively well over the next few years and they could make up good long term investments. Now because this is part of the Dow 30 series Well we’re picking we’re sticking with companies that are in the Dow Jones industrial average and that’s somewhat tricky because these are very large blue chip companies that have been around for a long time. So it’s going to leave out key growers like Facebook or Google that would easily make this list if they if we were not restricting ourselves to the Dow 30 companies. Okay our first sector is the financial sector. Now we actually have four different companies from the financial sector. First let’s look at both American Express and Visa. This is a chart of American Express is earnings going back the past couple of years and as we could see it’s been moving higher at a decent pace when we switch over to visa while visa has been doing even better than American Express. Now personally I think that these two companies are great additions to a growth portfolio because they’re likely to remain very important in the economy as technology pushes things forward even services like Venmo or Apple Pay or Samsung pay whatever it might be as they pick up ground they’re not leaving them. Visa and American Express behind there is simply incorporating those services into their own business. So I believe that Visa and American Express companies like that are gaining more ground and grinning gaining more importance. So I expect them to grow nicely in the coming years. Then we have the Travelers Companies now travelers are not actually using earnings per share. I’m using revenue because I think this belt better illustrates their growth potential and their growth over the past few years since earnings per share for insurance companies can be a bit deceptive. So on the revenue chart we can see that travelers is expected to pick up a decent amount of ground. We could see that with the green bars green bars our analyst estimates. So I think that this is likely to be a good thing for travelers stock as they continue to grow. Then we have the last company the financial sector. This is Goldman Sachs. Once again I use a different financial measure other than earnings per share. This is the last time I’m doing everything else going forward. The earnings per share here I use book value per share and I did this because if you remember that Goldman Sachs video well price to book value is a very popular way to try to value a financial stock like Goldman Sachs and Morgan Stanley or a company like that. So as you can see their book value per share has grown nicely and although we don’t have estimates for book value I believe that book value per share for Goldman will continue to do quite well in the coming years. Okay next up we have the information technology sector here we have two companies. First one is Apple. Now obviously Apple’s a solid company and they’re a good fit for most growth portfolios. And as we could see Apple’s earnings per share is growing and expected to continue to grow in the next few years. Apple is pushing to expand their current content offerings and this seems like a smart move going forward. Plus they always have their great products like their iPhones iPads things along those lines. So overall I expect as they continue to expand their content offerings Apple’s earnings per share and likely their stock price will continue to grow. Okay now right in line with this our next company is Microsoft. And as we could see Microsoft has started to pick up their earnings per share over the past few years. And we expect according to the green bars which is analyst estimates that they’re going to continue to grow in the coming years. I think Microsoft is one of the stronger companies out there. And I think that this makes a good addition to most growth portfolios. Okay. Now we slide over to the health care sector where we got two companies. The first one is Johnson of Johnson now Johnson and Johnson’s growth. Their earnings per share growth was a bit stale a few years ago leading up to about 2015 and the growth really started to pick up. And as we could see by analyst estimates while growth is expected to continue to grow for the next few years. So I think that this will make a good addition to the growth portfolio. Plus Johnson and Johnson is somewhat of a defensive company. So I think that that’s a nice way a nice thing we should incorporate since we’ve been on a bull run for so long. It’s probably good to have some defensive names in here. Okay. Next up we have UnitedHealth which is another defensive holding for our growth portfolio. And as we could see in their earnings per share. Sharp Well just like Johnson and Johnson they’ve begun to pick up speed recently and analysts estimates have their earnings per share continuing to grow which should make them a good addition to the growth portfolio. Plus like I said with JNJ they’re a defensive name they should be a defensive name. So in the event of a market pullback I think we would be happy that we added these two companies. Okay now we move over to the industrials but we have two more companies. The first one United Technologies now UTI ex is an interesting one because they’re in the middle of a merger with Raytheon and I believe that this could be a very good thing for UTI ex over the long run. And clearly we can see that their earnings per share estimates are supposed to they have been picking up pace in the next couple of years. So I think that this is going to make a solid growth has the potential to make a solid growth addition to our growth portfolio. Okay. Next up we have Boeing now Boeing is an interesting one and I’ve gone back and forth on this one. Now this is a chart of Boeing’s earnings per share going back the past few years and as we could see for 2019 Boeing’s EPA took a nosedive. Now this is an estimate because right now the first and second quarter for Boeing are already in but the third and fourth quarters are just estimates. So we’re making the whole thing an estimate. But either way in Q2 Boeing took a big loss after all the issues that they’ve run into with their planes and with many of the things that I’m sure we all know about going that that have happened recently but that dragged down their 20 19 estimates. But we add 20 20 well analysts estimates have them growing almost as if this didn’t happen. And I would expect solid growth after 2020 for at least a few more years which is why I think it would be smart to add Boeing to our growth portfolio. Okay next up we have consumer discretionary the first stock in the consumer discretionary sector is Home Depot. Now I’ve been a fan of Home Depot for a while and I believe they’ve been a solid growth stock and I expect for their growth to to remain relatively strong over the next few years. So once again I think that this is a nice addition to a growth portfolio in general. Okay. Next we have Nike. Now I actually think that Nike has done quite well in the past few years and I expect them to do well in the next few years as they try to revitalize their company. Now the trade tensions have weighed a bit on Nike and even though that most of their products are made in Vietnam I think it’s about 20 percent 25 percent is made in China. But that may be behind us now as a deal looks like it could be getting worked out either way I would expect for Nike’s earnings per share to continue to grow over the next couple years which could be a good thing for Nike stock and ultimately our growth portfolio. Okay. Next up we have Disney which is our only communication services company. Now as you could see on the earnings per share chart growth has somewhat stalled out making this a somewhat counterintuitive pick for a growth portfolio but I think that the stall has happened mostly because they’ve had to expend an excessive amount in their direct to consumer platforms recently plus they’ve had a call it a rough start to integrating the fox assets that they bought into their business but I expect this to be sorted out over the next year or two and then there’s somewhat sluggish growth should resume after that I believe over the long run Disney should do quite well. The earnings per share should do quite well and ultimately their stock and our growth portfolio because of it. Okay. So that wraps up all the companies from the Dow that I thought were a good addition to the growth portfolio at this time. Now there are a few other companies that could make interesting additions to this a company like Tesla as an example. I think we all know that they’ve had fantastic growth but they’re not in the Dow so I couldn’t included. I mentioned Facebook or Google. Those are companies that would definitely belong in a growth portfolio but not so much because they’re not in the Dow for our case. Now I could easily make a case for a company like Horizon and AT&T rises in the Dow AT&T isn’t that one I was borderline adding that to this but I expect there to be a lot of outlay of capital sort of like Disney was a few years ago I expect horizon to be having to do that for the next couple of years as they expand to 5G. So where I think that they will grow in the long run over the next decade or so. I believe that the companies here are more likely to grow sooner rather than later. So that’s our growth portfolio. Now my question to you is are there any Dow 30 companies that you think belong on this list that I shouldn’t. Would you have taken any off. I know that there’s tons of companies from let’s say the S&P 500 that should make a growth portfolio but since this was part of our Dow series I tried to limited to those. There’s also a few growth ETF s that could do quite well. Please let me know what you think in the comments below. Any companies that you would add or take away put those in the comments if you haven’t done so yet please hit the thumbs up on it really helps the channel and the video. And if you haven’t done so yet hit the subscribe button hit the bell icon. Thanks so much for stick with me all the way into the video and I’ll see you in the next video. Thanks.

Finance minister says gov’t will aim for growth of over 2.2% for 2020


Tanisha’s finance she laid out the
government’s ambitious goals for next year Hunan gives a 2.2 percent growth as
the 2020 target while renewing call for a fiscal expansion to revamp the economy
Kim has long shares with us his remarks finance minister Honam Yu said the
government aims to achieve economic growth next year of over 2.2 percent a
range of 2.2 to 2.3 percent is the growth forecast estimated by the IMF and
OECD out of briefing with reporters Monday to deliveries assessment of the
moon administration’s economic policy so far the finance minister said the
government will focus more on structural reform and boosting productivity for the
next two and a half years he said the government’s shift from policies focused
on growth to policies focused on inclusiveness and distribution has
helped strengthen the country’s social safety net but he said South Korea’s
growth has been hurt by slowing growth globally uncertainties like the us-china
trade dispute and the downturn in the semiconductor sector to boost growth and
investment he said the moon administration moving forward will focus
on structural reform and deregulation he added that the government will continue
with its expansionary fiscal policy a 2020 budget of over 440 billion u.s.
dollars which is up nine point three percent on your husband’s submitted to
the National Assembly detailed policy measures for next year will be announced
by December Tim Ezell Arirang news

Ex: Exponential Growth Function – Population


– A GROWING CITY HAD A
POPULATION OF 500,000 IN 2005, IN 2010 THE POPULATION
WAS 760,000. WE WANT TO ASSUME
EXPONENTIAL GROWTH AND THEN EXPRESS
THE POPULATION AFTER T YEARS AS A FUNCTION OF T, PREDICT THE POPULATION
IN 2025, AND THEN DETERMINE
IN WHICH YEAR THE POPULATION WILL REACH
1,000,000. SO WE WANT TO START BY FINDING
THE EXPONENTIAL FUNCTION THAT’S GOING TO MODEL
THIS POPULATION. SO WE’LL BE USING THIS
EXPONENTIAL FUNCTION HERE WHERE P OF T WOULD BE
THE POPULATION AFTER A CERTAIN NUMBER
OF YEARS, P SUB 0, OR P NOD, WOULD BE THE INITIAL
POPULATION, K WOULD BE
THE EXPONENTIAL GROWTH RATE, AND T WOULD BE THE TIME
IN YEARS. SO LETS START BY FINDING
THE EXPONENTIAL FUNCTION FOR THIS POPULATION. SO WHEN WE READ THESE
FIRST TWO SENTENCES, THE STARTING POPULATION
WOULD BE 500,000, SO P SUB 0 OR P NOD IS=TO
500,000, THIS IS IN 2005. AND THEN IN 2010
THE POPULATION WAS 760,000, SO P OF T WOULD BE
=TO 760,000. AND THEN FROM 205 TO 2010,
THAT’S A SPAN OF 5 YEARS, SO T IS GOING TO BE=TO 5. SO NOW WE’LL PERFORM
SUBSTITUTION INTO OUR EXPONENTIAL FUNCTION AND THEN SOLVE FOR K,
OUR EXPONENTIAL GROWTH RATE. SO WE WANT TO SOLVE
THE EQUATION, 760,000=500,000 x E
RAISED TO THE POWER OF K x T, BUT SINCE T IS 5,
WE’LL HAVE 5K. NOW, WE WANT TO SOLVE THIS
EXPONENTIAL EQUATION FOR K, SO WE’LL FIRST ISOLATE
THE EXPONENTIAL PART. SO WE’LL DIVIDE BOTH SIDES BY
500,000, THIS SIMPLIFIES TO 1. AND THEN ON THE LEFT SIDE
OF 760,000 DIVIDED BY 500,000, WHICH IS=TO 1.52. SO WE HAVE 1.52 WOULD=E
TO THE POWER OF 5K. AND NOW SINCE WE HAVE BASE E
HERE, INSTEAD OF TAKING
THE COMMON LOG OF BOTH SIDES, WE’LL TAKE THE NATURAL LOG
OF BOTH SIDES. AND NOW ON THE RIGHT SIDE
WE CAN APPLY THE POWER PROPERTY
OF LOG RHYTHMS TO MOVE THIS 5K TO THE FRONT. SO NOW WE’D HAVE NATURAL LOG
1.52=5K x NATURAL LOG E, BUT NATURAL LOG E IS=1. REMEMBER IF WE HAVE NATURAL
LOG E, THIS IS LOG BASE E, AND SINCE E RAISED
TO THE 1ST POWER IS=TO E, THIS IS=TO 1. SO THIS SIMPLIFIES TO 1. SO TO SOLVE THIS FOR K WE JUST NEED TO DIVIDE
BOTH SIDES BY 5. OF COURSE, WE COULD DIVIDE
BOTH SIDES BY NATURAL LOG E, BUT AGAIN THAT’S JUST=TO 1, SO IT’S NOT GOING
TO CHANGE ANYTHING. SO WE HAVE K
IS=TO THIS QUOTIENT, WHICH WE’LL HAVE TO GET
A DECIMAL APPROXIMATION FOR. SO WE HAVE NATURAL LOG OF 1.52
DIVIDED BY 5 AND THE MORE DECIMAL PLACES
THAT WE USE FOR K, THE MORE ACCURATE OUR ANSWER
IS GOING TO BE. LET’S GO AHEAD AND TAKE THIS
OUT TO 6 DECIMAL PLACES, SO WE’LL HAVE 0.083742. AND NOW WE HAVE
OUR EXPONENTIAL FUNCTION THAT’S GOING TO MODEL
THIS POPULATION. WE’LL HAVE P OF T IS=TO THE
INITIAL POPULATION OF 500,000 x E RAISED TO THE POWER
OF 0.083742 x T, WHERE T IS GOING TO BE
THE NUMBER OF YEARS AFTER THE YEAR 2005. SO LETS TAKE THIS FUNCTION
BACK TO THE PREVIOUS SCREEN. JUST KEEP IN MIND THAT T
IS THE NUMBER OF YEARS AFTER OUR BASE YEAR OF 2005. SO TO PREDICT THE POPULATION
IN 2025, WELL 2025 – THE BASE YEAR
OF 2005 WOULD BE 20. SO WE WANT TO FIND P OF 20
TO APPROXIMATE THE POPULATION IN THE YEAR 2025.   SO NOW WE’LL GO BACK
TO THE CALCULATOR AND APPROXIMATE THIS VALUE. SECOND NATURAL LOG BRINGS UP E RAISED TO THE POWER
OF .083742 x 20, THIS WOULD BE OUR EXPONENT
ON E, AND SO THE POPULATION IS GOING
TO BE APPROXIMATELY 2,668,971 IF WE ROUND
TO THE NEAREST PERSON. NOW, FOR THE LAST QUESTION
THEY WANT TO KNOW WHAT YEAR WILL THE POPULATION
REACH 1,000,000, SO WE WANT TO SUBSTITUTE
1,000,000 FOR P OF T AND SOLVE FOR T. SO WE’LL HAVE
1,000,000=500,000, E RAISED TO THE POWER
OF 0.083742T. SO WE’RE GOING TO ISOLATE
THE EXPONENTIAL PART. SO WE’LL DIVIDE BOTH SIDES
BY 500,000, THIS SIMPLIFIES TO ONE,
THIS WOULD BE 2, SO WE HAVE 2=E
RAISED TO THIS EXPONENT. AND JUST AS WE DID BEFORE, WE’LL NOW TAKE THE NATURAL LOG
OF BOTH SIDES OF THE EQUATION AND THEN APPLY THE POWER
OF PROPERTY OF LOG RHYTHMS. SO WE’LL MOVE THIS EXPONENT TO
THE FRONT OF THE LOG RHYTHM, SO WE’LL HAVE NATURAL LOG 2
=0.083472T x NATURAL LOG E, BUT AS WE SHOWED BEFORE
NATURAL LOG E SIMPLIFIES TO 1. SO SOLVE THIS FOR T, WE JUST NEED TO DIVIDE
BY THIS DECIMAL COEFFICIENT. AGAIN, THIS SIMPLIFIES TO 1 SO LET’S GO BACK
TO THE CALCULATOR. AND THIS QUOTIENT WOULD BE
THE VALUE OF T, WHICH WOULD BE THE NUMBER
OF YEARS AFTER 2005.   SO WE CAN SEE THAT T
IS APPROXIMATELY 8.28 YEARS.   SO THIS WOULD BE 8.28 YEARS
AFTER THE YEAR 2005, AND SINCE THE BASE YEAR
IS THE YEAR 2005, 2005 + 8.28 MEANS THAT THE POPULATION
WOULD REACH 1,000,000 DURING THE YEAR 2013.   OKAY, I HOPE YOU FOUND
THIS HELPFUL.