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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.

Respuesta :

lublana

Answer:

0.043

Step-by-step explanation:

We are given that

Initially when t=0

Then, A=22 million

The population of a country after t years is given by

[tex]A=22e^{kt}[/tex]

When t=8 then A=31 million

Substitute the values

[tex]31=22e^{8k}[/tex]

[tex]\frac{31}{22}=e^{8k}[/tex]

[tex]1.409=e^{8k}[/tex]

[tex]8k=ln(1.409)=0.343[/tex]

[tex]k=\frac{0.343}{8}=0.043[/tex]