Question

a new car is purchased for 20700 dollars. the value of the car depreciates at 11% per year. what will the value of the car be, to the nearest cent, after 11 years?

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 rate to decimal

The depreciation rate is 11%, so $r = \frac{11}{100} = 0.11$.

Step3: Substitute the values into the formula

We have $P = 20700$, $r = 0.11$, and $t = 11$. Plugging these into the formula gives $V = 20700(1 - 0.11)^{11}$.

Step4: Calculate $(1 - 0.11)$

$1 - 0.11 = 0.89$. So now we have $V = 20700(0.89)^{11}$.

Step5: Calculate $(0.89)^{11}$

Using a calculator, $(0.89)^{11} \approx 0.3056$.

Step6: Multiply by the initial price

$V = 20700 \times 0.3056 \approx 6325.92$.

Answer:

The value of the car after 11 years will be approximately $\$6325.92$.