question\na new car is purchased for 15500 do...
question\na new car is purchased for 15500 dollars. the value of the car depreciates at 7.5% per year. what will the value of the car be, to the nearest cent, after 6 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 time in years.
## Step2: Convert the rate to a decimal
Given $r = 7.5\%=0.075$, $P = 15500$, and $t = 6$.
## Step3: Substitute the values into the formula
$A=15500\times(1 - 0.075)^6$.
First, calculate $1-0.075 = 0.925$.
Then, calculate $(0.925)^6=0.925\times0.925\times0.925\times0.925\times0.925\times0.925\approx0.64797$.
Next, calculate $A = 15500\times0.64797\approx10043.54$.
# Answer:
$10043.54$