Im 2005, Bhutan had a population of about 2200000 and an annual growth factor of 1.0211. Let f(t) be the population t years after 2005 assuming growth continues at this rate.

Question

(a) Write a formula for f(t).

(b) According to your formula, what will the population of Bhutan be in 2012?

Answer 1

So again this is exponential, so we are expecting the formula to look like this: f(t) = a(b)^t where "a" is the initial value and "b" is the growth factor, or what it's multiplying each year "t". They tell us the initial population and growth factor.

So we know our equation should look like this:

f(t) = 2200000( 1.0211)^t

This is the answer to the first question. Part b is simply plugging in the number of years "t" after 2005. They tell us it's 2012. So how many years is 2012 after 2005? Should be 7 years. So we know 7 years have passed, so t = 7. Just plug that in for t and you'll get the answer.

f(7) = 2200000( 1.0211)⁷

Put that in a calculator, you'll get your answer.