Question

A population of 1,750 cheetahs decreases by 11% per year. How many cheetahs will there be in the population after 10 years? Round your answer to the nearest whole number. A.4969 B.486 C.164 D.546

Answer 1

`\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &1750\\ r=rate\to 11\%\to (11)/(100)\to &0.11\\ t=\textit{elapsed time}\to &10\\ \end{cases} \\\\\\ A=1750(1-0.11)^(10)\implies A=1750(0.89)^(10)\implies A\approx 545.68009877`