Question

The population of a particular country was 28 million in 1981; in 1994, it was 35 million. The exponential growth function A = 28ekt describes the population of this country t years after 1981. Use the fact that 13 years after 1981 the population increased by 7 million to find k to three decimal places.

Answer 1

`k = 0.017`

Explanation:

We have that

`A(t) = 28e^(kt)`

In which t is the number of years after 1981, and A is the population in the year t+1981.

So

Population of 35 million in 1994.

1994-1981 = 13.

So

A(13) = 35

`A(t) = 28e^(kt)`

`35 = 28e^(13k)`

`e^(13k) = 1.25`

Applying ln to both sides

`13k = 0.22`

`k = 0.017`