question a new car is purchased for 16600 dollars. the value of the car depreciates at 9.75% per year. what…

question a new car is purchased for 16600 dollars. the value of the car depreciates at 9.75% per year. what will the value of the car be, to the nearest cent, after 8 years?

question a new car is purchased for 16600 dollars. the value of the car depreciates at 9.75% per year. what will the value of the car be, to the nearest cent, after 8 years?

Answer

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, and $t$ is the time in years.

Step2: Substitute the given values

Here, $P=$16600$, $r = 0.0975$ (since $9.75%=0.0975$), and $t = 8$. $A=16600\times(1 - 0.0975)^8$

Step3: Calculate the value inside the parentheses

$1-0.0975 = 0.9025$

Step4: Calculate the power

$(0.9025)^8=0.9025\times0.9025\times0.9025\times0.9025\times0.9025\times0.9025\times0.9025\times0.9025\approx0.47097$

Step5: Calculate the final value of the car

$A = 16600\times0.47097\approx7818.10$

Answer:

$7818.10$