Question

An animal reserve 24,000 elk.The population is increasing at a rate of 13 percent per year.How long will it take for the population to reach 72,000?If necessary, round your answer to the nearest tenth. The population will reach 72,000 in approximately years

Answer 1

9.0 years

Explanation:

The exponential equation for the population can be written as ...

population = (initial population)(1 +growth rate)^t

p = 24000(1.13^t)

We want this to be 72000, so ...

72000 = 24000(1.13^t)

Dividing by 24000 gives ...

3 = 1.13^t

Taking logs, we have ...

log(3) = t·log(1.13)

log(3)/log(1.13) = t ≈ 8.98

It will take about 9.0 years for the elk population to reach 72,000.