a new car is purchased for 19900 dollars. the value of the car depreciates at 7.5% 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 amount, $r$ is the rate of decay as a decimal, and $t$ is the time in years.

Step2: Convert the rate to a decimal

The rate of depreciation $r = 7.5%=0.075$, the initial value of the car $P = 19900$, and the time $t = 8$ years.

Step3: Substitute the values into the formula

$A=19900\times(1 - 0.075)^8$. First, calculate $1-0.075 = 0.925$. Then, calculate $(0.925)^8\approx0.569777$. Next, multiply by the initial value: $A = 19900\times0.569777\approx11338.56$.

Answer:

$11338.56$