Question

5. A mouse population is 25,000 and is decreasing at a rate of 20% per year. Write anexponential function to model the situation. Enter your answer in the form y = a(b)^x

Answer 1

Given:

Using the population decrease formula,

`\begin{gathered} y=ab^x \\ where:b=1-r.....................(decreasing\text{ population\rparen} \\ \\ Hence, \\ y=a(1-r)^x \end{gathered}`

where:

`\begin{gathered} a=25000 \\ r=(20)/(100)=0.2 \\ y=a(1-r)^x \\ y=25000(1-0.2)^x \\ y=25000(0.8)^x \end{gathered}`

Therefore, the exponential function is;

`y=25000(0.8)^x`