question a new car is purchased for 17600 dollars. the value of the car depreciates at 11.75% per year. what…

question a new car is purchased for 17600 dollars. the value of the car depreciates at 11.75% per year. what will the value of the car be, to the nearest cent, after 11 years?

question a new car is purchased for 17600 dollars. the value of the car depreciates at 11.75% per year. what will the value of the car be, to the nearest cent, after 11 years?

Answer

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 percentage to a decimal

The rate of depreciation $r = 11.75%=0.1175$, the initial value of the car $P = 17600$, and the time $t = 11$ years.

Step3: Substitute the values into the formula

$A=17600\times(1 - 0.1175)^{11}$. First, calculate $1-0.1175 = 0.8825$. Then, calculate $(0.8825)^{11}$. Using a calculator, $(0.8825)^{11}\approx0.28777$. Next, multiply by the initial value: $A = 17600\times0.28777$. $A\approx5064.75$.

Answer:

$5064.75$