Question

Tua bought a new car. The value of the car decreases exponentially each year. The value of the car after 3 years is $39,366. After 5 years, the value is $31,886.46.How much did Tua originally pay for the car?(1 point)Responses$54,000$54,000$43,740$43,740$71,252.46$71,252.46$39,366$39,366

Answer 1

Let the original price be P and annual decay factor r. Then
P r^3 = 39,366 and P r^5 = 31,886.46.
Divide to get r^2 = 31,886.46 / 39,366 = 0.81, so r = 0.9.
Then P = 39,366 / 0.9^3 = 39,366 / 0.729 = $54,000.