a new car is purchased for 25000 dollars. the value of the car depreciates at 8.25% per year. what will the…

a new car is purchased for 25000 dollars. the value of the car depreciates at 8.25% per year. what will the value of the car be, to the nearest cent, after 15 years? answer attempt 1 out of 2

a new car is purchased for 25000 dollars. the value of the car depreciates at 8.25% per year. what will the value of the car be, to the nearest cent, after 15 years? answer attempt 1 out of 2

Answer

Answer:

$7075.05$

Explanation:

Step1: Identify the formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the time in years.

Step2: Convert the rate to a decimal

Given $r = 8.25%=0.0825$, $P = 25000$, and $t = 15$.

Step3: Substitute values into the formula

$A=25000\times(1 - 0.0825)^{15}$.

Step4: Calculate the value inside the parentheses

$1-0.0825 = 0.9175$.

Step5: Calculate the power

$(0.9175)^{15}\approx0.283$.

Step6: Calculate the final value

$A = 25000\times0.283 = 7075.05$.