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 principal (initial value), $r$ is the annual depreciation rate (as a decimal), and $t$ is the time in years.

Step2: Plug in the given values

We have $P = 20700$, $r = 0.11$ (since 11% = 0.11), and $t = 11$. So we substitute these into the formula: $V = 20700(1 - 0.11)^{11}$.

Step3: Calculate $(1 - 0.11)$

First, calculate $1 - 0.11 = 0.89$.

Step4: Calculate $0.89^{11}$

Using a calculator, $0.89^{11}\approx0.3057$.

Step5: Calculate the final value

Multiply this by the initial value: $V = 20700\times0.3057\approx6327.99$.

Answer:

The value of the car after 11 years will be approximately $\$6327.99$.