Question

The elephant population of a nature preserve since 1990 is modeled by the exponential function f(x)=315⋅1.075x
. Find the elephant population in 1990 and the percentage at which the population increases each year.(1 point)
Responses

The elephant population in 1990 is 339, and the population increases by 7.5% each year.
The elephant population in 1990 is 339, and the population increases by 7.5% each year.

The elephant population in 1990 is 315, and the population increases by 0.75% each year.
The elephant population in 1990 is 315, and the population increases by 0.75% each year.

The elephant population in 1990 is 315, and the population increases by 7.5% each year.
The elephant population in 1990 is 315, and the population increases by 7.5% each year.

The elephant population in 1990 is 315, and the population increases by 1.075% each year.
The elephant population in 1990 is 315, and the population increases by 1.075% each year.

Answer 1

The correct choice is: The elephant population in 1990 is 315, and the population increases by 7.5% each year.

Reason: f(0)=315·1.075^0=315, and the growth factor 1.075 corresponds to a 7.5% annual increase.