Question

The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by about 7.2% per year. Use an exponential decay function to approximate the population in 2036 to the nearest hundred. Enter your answer in the box.

Answer 1

The estimated Rabbit population by the year 2036 is 32,309 rabbits

Explanation:

In this question, we are expected to use the exponential decay function to estimate population of rabbits in a certain year.

An exponential decay function refers to an equation that estimates the value of a parameter(dependent parameter) at a certain value of the independent parameter given that the independent parameter decreases at a certain constant rate.

Firstly, what we need to do is to write the decay function. To do this, we shall be representing the population by variable P, the rate by r , the number of years by t and the initial population by I

Mathematically, we have the decay function as;

P = I(1-r)^t

From the question, we identify these values as;

P = 144,000 : r = 7.2% = 7.2/100 = 0.072, I = 144,00 and t = 2036-2016 = 20 years

Let's plug these values;

P = 144,000(1-0.072)^20

P = 144,000(0.928)^20

P= 32,309