Question

Natalie is buying a car at 9800. The value drops 5% each year. What is the value of the car in 8 years

Answer 1

Answer: 6,502

Step-by-step explanation: 9,800(1-0.05)^8 = 6,502

Answer 2

`\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &9800\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ t=\textit{elapsed time}\dotfill &8\\ \end{cases} \\\\\\ A = 9800(1 - 0.05)^(8) \implies A=9800(0.95)^8\implies A \approx 6501.52`