Question

A $5,000 television depreciates by 14.8% each year. How much will the television be worth in 7 years?

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 &5000\\ r=rate\to 14.8\%\to (14.8)/(100)\dotfill &0.148\\ t=years\dotfill &7 \end{cases} \\\\\\ A = 5000(1 - 0.148)^(7) \implies A = 5000( 0.852 )^(7)\implies A \approx 1629.47`