a new car is purchased for 17500 dollars. the value of the car depreciates at 7.25% per year. to the nearest…

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time. Here, $P = 17500$, $r=0.0725$, and $A = 9600$. So the equation becomes $9600=17500(1 - 0.0725)^t$.

Step2: Simplify the equation

First, divide both sides of the equation by $17500$: $\frac{9600}{17500}=(0.9275)^t$. So, $0.548571=(0.9275)^t$.

Step3: Take the natural - logarithm of both sides

$\ln(0.548571)=t\ln(0.9275)$.

Step4: Solve for $t$

$t=\frac{\ln(0.548571)}{\ln(0.9275)}$. We know that $\ln(0.548571)\approx - 0.600$ and $\ln(0.9275)\approx-0.075$. Then $t=\frac{- 0.600}{-0.075}=8$.

Answer:

$8$