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exponential funtions

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The Population size of a country was 12.7 million in the year 2000 and 14.3 million in the year 2010. Assume that the population size follows an exponential function. 

What will the population size be in the year 2015, assuming the formula holds until then?

When will the population reach 18 million?

Oct 23rd, 2017

the rate of growth is (14.3 - 12.7) / 12.7 /10 = 0.0126  because it increased 12.6% over a 10 year period

Then we use the formula

P final = P initial x e^rt  where r is the growth rate and t is the number of years.

So, in the year 2015 the population will be

P = 12.7e^0.0126*15

= 15.3 million

To calculate when it will reach 18 million:

18 = 12.7e^0.0126*t

1.4173 = e^0.0126t

ln1.4173 = 0.0126t

t = ln1.4173 / 0.0126 = 27.7 years

Apr 16th, 2015

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