Question

a new car is purchased for 15300 dollars. the value of the car depreciates at 14.25% per year. what will the value of the car be, to the nearest cent, after 6 years?

Explanation:

Step1: Recall the depreciation formula

The formula for exponential depreciation is $V = P(1 - r)^t$, where $V$ is the final value, $P$ is the initial principal (value), $r$ is the annual depreciation rate (in decimal), and $t$ is the time in years.
First, convert the depreciation rate from percentage to decimal: $r = 14.25\% = 0.1425$.

Step2: Identify the given values

We have $P = 15300$ dollars, $r = 0.1425$, and $t = 6$ years.

Step3: Substitute the values into the formula

Substitute $P$, $r$, and $t$ into the formula $V = P(1 - r)^t$:
$V = 15300\times(1 - 0.1425)^6$
First, calculate $(1 - 0.1425) = 0.8575$.
Then, calculate $0.8575^6$. Using a calculator, $0.8575^6\approx0.3957$.

Step4: Calculate the final value

Multiply $15300$ by $0.3957$: $V = 15300\times0.3957\approx6054.21$.

Answer:

The value of the car after 6 years will be approximately $\$6054.21$.