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.P(t) = _______________, so in 2036 the population is about _________ rabbits.

Answer 1

P(t) = 32308.88, so in 2036 the population is about 32309 rabbits.​

Step-by-step explanation:

An exponential decay function has the following form:

`P(t)=P_0(1-r)^t`

Where P0 is the initial value, r is the percentage of decrease and t is the number of years.

If the population decrease 7.2% every year and the population in 2016 was 144,000, then we can write the function as:

`P(t)=144000(1-0.072)^t`

Where t is the number of years since 2016. So, if we want to approximate the population in 2036, we need to calculate the number of years between 2036 and 2016 as:

2036 - 2016 = 20 years.

Therefore, replacing t by 20, we get that the population in 2036 will be:

`\begin{gathered} P(20)=144000(1-0.072)^(20) \\ P(20)=32308.88 \end{gathered}`

So, the answer is:

P(t) = 32308.88, so in 2036 the population is about 32309 rabbits.​