Question

Chuy purchased a used truck for

$11,500. According to an online
vehicle website, his truck will
depreciate, or lose value, at a rate of
5.5% each year. What function, d(x),
represents the value of Chuy's truck
x years after its purchase?

Answer 1

d(x) = 11500*0.945^x

Explanation:

Chuy's truck loses 5.5% of its value each year. That means each year:

(current worth of truck) = (previous year's worth) - (previous year's worth)*5.5%

The current worth is also equivalent to (previous year's worth)*94.5%.

After one year, the worth is (first year)*94.5%.

After two years, the worth is ((first year)*94.5%)*94.5%.

Note that each year, the original value of the car is multiplied by 94.5% to get the current worth. Recall also that 94.5% = 0.945.

d(x) = 11500*0.945^x, where 11500 is the original price.