a new car is purchased for 21100 dollars. the value of the car depreciates at 10.5% 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 $r = 10.5%=0.105$, $P = 21100$, and $t = 6$.

Step3: Substitute the values into the formula

$A=21100\times(1 - 0.105)^6$. First, calculate $1-0.105 = 0.895$. Then, calculate $(0.895)^6=0.895\times0.895\times0.895\times0.895\times0.895\times0.895\approx0.56477$. Next, calculate $A = 21100\times0.56477\approx11916.65$.

Answer:

$11916.65$