question\na new car is purchased for 25000 do...
question\na 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
# 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 number of years.
Here, $P=\$25000$, $r = 0.0825$, and $t = 15$.
## Step2: Substitute the values into the formula
$A=25000\times(1 - 0.0825)^{15}$.
First, calculate $1-0.0825 = 0.9175$.
Then, find $(0.9175)^{15}$. Using a calculator, $(0.9175)^{15}\approx0.28477$.
## Step3: Calculate the final value
$A = 25000\times0.28477=\$7119.25$.
# Answer:
$7119.25$