question\na new car is purchased for 15500 dollars. the value of the car depreciates at 7.5% per year. what…

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 $r = 7.5%=0.075$, $P = 15500$, and $t = 6$.

Step3: Substitute the values into the formula

$A=15500\times(1 - 0.075)^6$. First, calculate $1-0.075 = 0.925$. Then, calculate $(0.925)^6=0.925\times0.925\times0.925\times0.925\times0.925\times0.925\approx0.64797$. Next, calculate $A = 15500\times0.64797\approx10043.54$.

Answer:

$10043.54$