Question

A population of 510,000 toads is expected to shrink at a rate of 6.2% per year. Which is the best prediction for the toad population in 18 years?

a. 478,380
b. 316,200
c. 161,147
d. 86,108

Answer 1

P=510,000×(1−0.062)^(18)
P=161,147

Answer 2

Answer: c. 161,147

Explanation:

The exponential decay function with rate of decay r in x years is given by :-

`y=A(1-r)^x`, where A is the initial population.

Given : Initial population of toads= 510,000

The rate of decay = 6.2%= 0.062

The population of toads after 18 years is given by :-

`y=510,000(1-0.062)^(18)\\\\=510,000(0.938)^(18)\\\\=161,146.644552\approx161,147`

Hence, the best prediction for the toad population in 18 years is 161,147.