a new car is purchased for 20300 dollars. the value of the car depreciates at 8.75% per year. what will the…

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 $r = 8.75%=0.0875$, $P = 20300$, and $t = 12$.

Step3: Substitute the values into the formula

$A=20300\times(1 - 0.0875)^{12}$. First, calculate $1-0.0875 = 0.9125$. Then, calculate $(0.9125)^{12}$. Using a calculator, $(0.9125)^{12}\approx0.34777$. Next, multiply by the initial value: $A = 20300\times0.34777$. $A\approx20300\times0.34777 = 7059.731$.

Answer:

$7059.73$