Question

At the beginning of an environmental study, a forest covered an area of 1500 km. Since then, this area has decreased by 7.25% each year

Let t be the number of years since the start of the study let y be the area that the forest covers in km?

Write an exponential function showing the relationship between y and t

Answer 1

`\qquad \textit{Amount for Exponential Decay} \\\\ y=P(1 - r)^t\qquad \begin{cases} y=\textit{current amount}\\ P=\textit{initial amount}\dotfill &1500\\ r=rate\to 7.25\%\to (7.25)/(100)\dotfill &0.0725\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ y=1500(1-0.0725)^t\implies y=1500(0.9275)^t`