Question

There are 185 deer in a state park. The population is increasing at the rate of 16% per year. Enter a

prediction for how long it will take the population to reach 305. If necessary, round your answer to the nearest tenth.

The deer population will reach 305 in approximately _____
years.

Answer 1

Approximately 3.4 years more or less

Explanation:

If we represent this exponential growth as P=185(1.16)^n where n is the number of years passed and P is the population, then:

P=185(1.16)^n

305=185(1.16)^n

1.65=1.16^n

log₁.₁₆(1.65)=log₁.₁₆(1.16^n)

3.37=n

So the deer population will reach 305 in approximately 3.4 years.