question\na new car is purchased for 17000 dollars. the value of the car depreciates at 13.5% per year. what…

question\na new car is purchased for 17000 dollars. the value of the car depreciates at 13.5% per year. what will the value of the car be, to the nearest cent, after 12 years?\nanswer attempt 1 out of 2

question\na new car is purchased for 17000 dollars. the value of the car depreciates at 13.5% per year. what will the value of the car be, to the nearest cent, after 12 years?\nanswer attempt 1 out of 2

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. Here, $P=$17000$, $r = 0.135$, and $t = 12$.

Step2: Substitute the values into the formula

$A=17000\times(1 - 0.135)^{12}$. First, calculate $1-0.135 = 0.865$. Then, find $(0.865)^{12}$. Using a calculator, $(0.865)^{12}\approx0.18477$.

Step3: Calculate the final value

$A = 17000\times0.18477=3141.09$.

Answer:

$3141.09$