Question

The population of a particular country was 23 million in 1982; in 1995, it was 33 million. Theexponential growth function A =23ekt describes the population of this country t years after 1982.Use the fact that 13 years after 1982 the population increased by 10 million to find k to threedecimal places.

Answer 1

The value of k is 0.448.

Explanation:

Given the exponential growth function is

`A=23e^(kt)`

A= The population of the country

k= growth rate.

The population of the country increased by 10 million in 13 years after 1982.

Then the population is =(23+13)million = 36 million.

Here,

A= 36 million, t= 13

`A=23e^(kt)`

`\Rightarrow 36=23e^(13k)`

`\Rightarrow e^(13k)=(36)/(23)`

Taking ln function both sides

`\Rightarrow ln|e^(13k)|=ln|(36)/(23)|`

`\Rightarrow {13k}=ln|(36)/(23)|`

`\Rightarrow {k}=(ln|(36)/(23)|)/(13)`

`\Rightarrow k=0.448`

The value of k is 0.448.