Question

An equation for the depreciation of a car is given by y = A(1 – r)t, where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year. How old is the car?

Answer 1

The answer is 3 years

Answer 2

The age of the car is 3 years old.

Original Value = $20,000.

Depreciation = 15 %.

Time = t (Assume).

Current value = $12,282.50

The general equation for depreciation is given by $y=A(1-r)^t.$

y = current value.

A = original cost.

r = rate of depreciation.

and t = time in years.

We need to determine how old the car is if its current value is $12,282.2.

Therefore,

$\begin{aligned}y&=A(1-r)^t\\12282.5&=20000(1-.15)^t\\0.614125&=(0.85)^t\\0.614125&=(0.85 \times 0.85)^{t/2}\\0.614125&=0.7225^{t/2}\\0.614125&=(0.7225 \times 0.85)^{t/3}\\0.614125&=0.614125^{t/3}\\\dfrac{t}{3}&=1\\t&=3\end{aligned}$

Thus, the age of the car is 3 years.

To know more about the depreciation, please refer to the link:

brainly.com/question/3492150