Question

exponential functions - basic
this is the only question in this section.
question
a new car is purchased for 25000 dollars. the value of the car depreciates at 8.25% per year. what will the value of the car be, to the nearest cent, after 15 years?
answer attempt 4 out of 5

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, \( P=\$25000 \), \( r = 8.25\%=0.0825 \), and \( t = 15 \) years. So the formula becomes \( A=25000\times(1 - 0.0825)^{15} \).

Step3: Calculate \( 1 - r \)

\( 1-0.0825=0.9175 \)

Step4: Calculate the power

\( 0.9175^{15}\approx0.284797 \)

Step5: Calculate \( A \)

\( A = 25000\times0.284797=\$7119.93 \)

Answer:

\( 7119.93 \)