Question

the population of mice in hooville is decreasing at a rate of 2%. The current mouse population is 750,000. Write the function to represent the population of the mice in Hooville.

Answer 1

$\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &750000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ A=750000(1-0.02)^t\implies A=750000(0.98)^t$