Question

The population of a particular country was 22 million in 1985; in 1993, it was 31 million. The exponential growth function A=22e^kt describes the population of this country t years after 1985. Use the fact that 8 years after 1985 the population increased by 9 million to find k to three decimal places.

Answer 1

0.043

Explanation:

We are given that

Initially when t=0

Then, A=22 million

The population of a country after t years is given by

`A=22e^(kt)`

When t=8 then A=31 million

Substitute the values

`31=22e^(8k)`

`(31)/(22)=e^(8k)`

`1.409=e^(8k)`

`8k=ln(1.409)=0.343`

`k=(0.343)/(8)=0.043`