Question

After the last ice age began, the number of animal species in Australia changed rapidly.

The relationship between the elapsed time, t, in years, since the ice age began, and the total number of animal species, S(t), is modeled by the following function:
S(t)=4,200,000⋅(0.72)t

Complete the following sentence about the yearly percent change of the number of animal species.

Every year, _______ percent of species are SUBTRACTED/ADDED from the total number of animal species.

Answer 1

Every year 28 percent of species are SUBTRACTED from the total number of animal species.

Explanation:

Exponential growth or decay:

The equation for exponential growth or decay has the following format:

`A(t) = A(0)(1+r)^t`

In which A(0) is the initial amount and r is the growth/decay rate, as a decimal.

If r > 0, each year r percent is added to the total number, and if r < 0, each year, r percent is decreased from the total number.

In this question:

`S(t) = 4200000(0.72)^t`

So

`1 - r = 0.72`

`r = 0.72 - 1 = -0.28`

Thus

Every year 28 percent of species are SUBTRACTED from the total number of animal species.