Question

The value of a machine depreciates each year by 5% of its value at the beginning of that year. If its value when new on 1st January 1980 was # 10,250. 00, what was its value in January 1989 when its was 9years old. Give your answer correct to three significant figures.

Answer 1

$\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &10250\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\textit{elapsed time}\dotfill &9\\ \end{cases} \\\\\\ A=10250(1 - 0.05)^{9}\implies A=10250(0.95)^9\implies A\approx 6460$