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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.

Respuesta :

Answer:

[tex]k = 0.017[/tex]

Step-by-step explanation:

We have that

[tex]A(t) = 28e^{kt}[/tex]

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

[tex]A(t) = 28e^{kt}[/tex]

[tex]35 = 28e^{13k}[/tex]

[tex]e^{13k} = 1.25[/tex]

Applying ln to both sides

[tex]13k = 0.22[/tex]

[tex]k = 0.017[/tex]

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