a new car is purchased for 16600 dollars. the...
a new car is purchased for 16600 dollars. the value of the car depreciates at 9.75% per year. what will the value of the car be, to the nearest cent, after 8 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
Given $r = 9.75\%=0.0975$, $P = 16600$, and $t = 8$.
## Step3: Substitute the values into the formula
$A=16600\times(1 - 0.0975)^8$.
First, calculate $1-0.0975 = 0.9025$.
Then, calculate $(0.9025)^8$. Using a calculator, $(0.9025)^8\approx0.47077$.
Next, multiply by the initial value: $A = 16600\times0.47077$.
$A\approx7814.78$.
# Answer:
$7814.78$