Question

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? watch video show examples

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.
Here, $P = 15300$, $r = 0.1425$ (since 14.25% = 0.1425), and $t = 6$.

Step2: Substitute the values into the formula

Substitute $P = 15300$, $r = 0.1425$, and $t = 6$ into the formula:
$V = 15300(1 - 0.1425)^6$
First, calculate $1 - 0.1425 = 0.8575$.
Then, calculate $0.8575^6$. Let's compute this step by step:
$0.8575^2 = 0.8575 \times 0.8575 \approx 0.7353$
$0.8575^4 = (0.7353)^2 \approx 0.5407$
$0.8575^6 = 0.8575^4 \times 0.8575^2 \approx 0.5407 \times 0.7353 \approx 0.3976$
Now, multiply by $15300$:
$V \approx 15300 \times 0.3976 \approx 6083.28$

Answer:

The value of the car after 6 years, to the nearest cent, is $\$6083.28$.