Question

a new car is purchased for 17600 dollars. the value of the car depreciates at 11.75% 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: Convert the depreciation rate to a decimal

The depreciation rate is $11.75\%$, so $r = \frac{11.75}{100} = 0.1175$.

Step3: Substitute the given values into the formula

We know that $P = 17600$, $r = 0.1175$, and $t = 11$. Substituting these into the formula gives:

$$
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$$

Step4: Calculate $(0.8825)^{11}$

Using a calculator, we find that $(0.8825)^{11}\approx0.2744$.

Step5: Calculate the final value

Multiply this result by the initial value:

$$ V = 17600\times0.2744\approx4829.44 $$

Answer:

The value of the car after 11 years will be approximately $\$4829.44$.