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

question 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

question 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

Explanation:

Step1: Identify the depreciation formula

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

Step2: Convert the rate to a decimal

The rate of depreciation $r = 8.25%=0.0825$, the initial value $P = 25000$ dollars, and the time $t = 15$ years.

Step3: Substitute the values into the formula

$A=25000\times(1 - 0.0825)^{15}$. First, calculate $1-0.0825 = 0.9175$. Then, calculate $(0.9175)^{15}$. Using a calculator, $(0.9175)^{15}\approx0.28477$. Next, multiply by the initial value: $A = 25000\times0.28477 = 7119.25$.

Answer:

$7119.25$