Use Multiplication Properties of Exponents · Exercise 81

Depreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be \ 20,000 \left(0.90\right)$andthevalueofthecaraftertheendofthesecondyearwouldbe$$ 20,000 \left(0.90\right)^{2}$. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.

\begin{array}{|c|c|}\hline \text{Year} & \text{Cost} \\ \hline \text{1} & \\text{ 20,000 left(0.90right)$} \\ \hline \text{2} & \\text{ 20,000 left(0.90right)^2$} \\ \hline \text{3} & \\ \hline \text{…} & \text{…} \\ \hline \text{8} & \text{?} \\ \hline\end{array}

This problem refers to a figure in its source book that isn't reproduced here.

OpenStax, Elementary Algebra 2e · §6.2 Use Multiplication Properties of Exponents · Exercise 81