Question

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.

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

Answer 2

The value of k is 0.05.

The exponential growth function is: A = 28e^kt

Where

A = future value of population

e = 2.718

k = growth rate

t = time

The  exponential growth function can be written as:

36 = 28 x e^k 5

log(36/28) ÷ log(e) ÷ 5 = 0.05

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