Exponential growth function problem?

Question

The population of a particular country was 24 million in 1982; in 1997, it was 29 million. The

exponential growth function A =24ekt describes the population of this country t years after 1982.

Use the fact that 15 years after 1982 the population increased by 5 million to find k to three decimal

places.

 

I'm not sure where the numbers go, I think i'm confused by the wording. Thank you!

Answer 1

A: population, in millions

e: Euler's number

k: exponential rate of increase

t: number of years after 1982

 

Putting the numbers into the equation, you get:

 

29=24e^(15k)

 

Divide both sides by 24 and take the natural logarithm of both sides:

 

ln(29/24)=15k

 

Then divide both sides by 15:

 

k=ln(29/24)/15

 

Using a calculator, we see that k is approximately 0.013.

 

I hope this helps!