Question

question
a new car is purchased for 20700 dollars. the value of the car depreciates at 11% per year. what will the value of the car be, to the nearest cent, after 11 years?

Explanation:

Step1: Identify the formula

The formula for exponential decay is \(A = P(1 - r)^t\), where \(P\) is the initial amount, \(r\) is the rate of decay, and \(t\) is the time.

Step2: Substitute the values

Here, \(P=\$20700\), \(r = 0.11\), and \(t = 11\). So, \(A=20700\times(1 - 0.11)^{11}\).

Step3: Calculate \((1 - 0.11)^{11}\)

\(1-0.11 = 0.89\). Then \(0.89^{11}\approx0.2959\) (using a calculator).

Step4: Calculate \(A\)

\(A = 20700\times0.2959\). \(20700\times0.2959=20700\times(0.3 - 0.0041)=20700\times0.3-20700\times0.0041 = 6210-84.87=6125.13\).

Answer:

\(6125.13\)