a new car is purchased for 20800 dollars. the value of the car depreciates at 10.75% 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 number of years.

Step2: Convert the rate to a decimal

Given $r = 10.75%=0.1075$, $P = 20800$, and $t = 13$.

Step3: Substitute the values into the formula

$A=20800\times(1 - 0.1075)^{13}$. First, calculate $1-0.1075 = 0.8925$. Then, calculate $(0.8925)^{13}\approx0.24777$. Finally, $A = 20800\times0.24777\approx5153.62$.

Answer:

$5153.62$