a new car is purchased for 16400 dollars. the value of the car depreciates at 12.5% per year. what will the…

Explanation:

Step1: Identify the formula for depreciation

The formula for exponential depreciation is $V = P(1 - r)^t$, where $V$ is the final value, $P$ is the initial principal (purchase price), $r$ is the annual depreciation rate (as a decimal), and $t$ is the time in years.

Step2: Convert the depreciation rate to a decimal

The depreciation rate is 12.5%, which is $0.125$ in decimal form. So, $1 - r = 1 - 0.125 = 0.875$.

Step3: Substitute the values into the formula

We have $P = 16400$, $r = 0.125$, and $t = 8$. Substituting these into the formula $V = P(1 - r)^t$, we get $V = 16400\times(0.875)^8$.

Step4: Calculate $(0.875)^8$

First, calculate $(0.875)^8$. Using a calculator, $(0.875)^8\approx0.3403991792$.

Step5: Calculate the final value

Multiply this result by 16400: $V = 16400\times0.3403991792\approx5582.55$.

Answer:

The value of the car after 8 years will be approximately $$5582.55$.