Question

The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by about 7.2% per year. Write an exponential decay function, P(t), and use it to approximate the population in 2036.

Answer 1

Hello!

The answer is:

In 2036 there will be a population of 32309 rabbits.

Why?

We can calculate the exponential decay using the following function:

$P(t)=StartAmount*(1-\frac{percent}{100})^{t}$

Where,

Start Amount, is the starting value or amount.

Percent, is the decay rate.

t, is the time elapsed.

We are given:

$StartAmount=144,000\\x=7.2(percent)\\t=2036-2016=20years$

Now, substituting it into the equation, we have:

$P(t)=StartAmount(1-\frac{percent}{100})^{t}$

$P(t)=144000*(1-\frac{7.2}{100})^{20}$

$P(t)=144000*(1-0.072)^{20}$

$P(t)=144000*(0.928)^{20}$

$P(t)=144000*(0.928)^{20}$

$P(t)=144000*0.861=32308.888=32309$

Hence, we have that in 2036 the population of rabbis will be 32309 rabbits.

Have a nice day!