The population of a particular country was 28 million in 1985; in 1990, it was 36 million. The exponential growth function A=28e^{kt} describes the population of this country t years after 1985. Use the fact that 5 years after 1985 the population increased by 8 million to find k to three decimal places.

Question

Mathematics

Salvatore Riggs

11 September, 23:44

The population of a particular country was 28 million in 1985; in 1990, it was 36 million. The exponential growth function A=28e^{kt} describes the population of this country t years after 1985. Use the fact that 5 years after 1985 the population increased by 8 million to find k to three decimal places.

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Rhianna Craig · Answer 1

A=28e^ (kt)

A = 36 million

T=5 years (1990-1985)

36=28e^ (5k)

Solve for k

First divide each side by 28 to get

36/28=e^ (5k)

Take the log

Log (36/28) = 5k*log (e)

5k=log (36/28) : log (e)

K=[log (36/28) : log (e) ]:5

K=0.05