a new car is purchased for 16400 dollars. the value of the car depreciates at 8.25% 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 percentage to a decimal

Given $r = 8.25%=0.0825$, $P = 16400$, and $t = 10$.

Step3: Substitute the values into the formula

$A=16400\times(1 - 0.0825)^{10}$. First, calculate $1-0.0825 = 0.9175$. Then, calculate $(0.9175)^{10}$. Using a calculator, $(0.9175)^{10}\approx0.43477$. Next, multiply by the initial value: $A = 16400\times0.43477$. $A=16400\times0.43477 = 7130.228$.

Answer:

$7130.23$