a new car is purchased for 16600 dollars. the value of the car depreciates at 9.75% 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 $r = 9.75%=0.0975$, $P = 16600$, 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:

$7814.78$