Question

You buy a used car for \(\$ 7000\). The car depreciates at the rate of \(6 \%\) per year. Find the value of the car in the given years. 10 years

Short answer

The value of the car after 10 years is approximately \$4174.74

Step-by-step solution

Understand the problem

The initial cost of the car is \$7000 and it depreciates at a rate of 6% per year. We are required to find the value of the car in 10 years. This is an example of exponential decay, or a decreasing exponential function.

Formulate the depreciation function

The value \( V \) of the car after \( t \) years can be evaluated using the exponential decay function: \( V(t) = P(1 - r) ^ t \). Where: \( P = \$7000 \) (initial value), \( r = 6 \% = 0.06 \) (rate of depreciation per year), \( t \) is the time in years.

Calculate the value of the car in 10 years

Substitute the values into the function, so we get: \( V(10) = \$7000(1 - 0.06) ^ {10} \). Using a calculator to approximate, the value of the car after 10 years would be \$4174.74