Question
Sydney bought a new car for $32,000.00. If the car depreciates in value by 8% each year, the situation can be modeled by the function f(x)=32,000(0.92)x
. Complete the table to find the value of the car to the nearest cent after three years.
(1 point)
The value of the car after three years is $
.
. Complete the table to find the value of the car to the nearest cent after three years.
(1 point)
The value of the car after three years is $
.
Answers
GPT-4o mini
To find the value of the car after three years using the function \( f(x) = 32,000(0.92)^x \), we will substitute \( x = 3 \) into the function.
\[
f(3) = 32,000(0.92)^3
\]
First, calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now, multiply this by 32,000:
\[
f(3) = 32,000 \times 0.778688 \approx 24,980.00
\]
Therefore, the value of the car after three years is approximately:
\[
\text{The value of the car after three years is } \$24,980.00.
\]
\[
f(3) = 32,000(0.92)^3
\]
First, calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now, multiply this by 32,000:
\[
f(3) = 32,000 \times 0.778688 \approx 24,980.00
\]
Therefore, the value of the car after three years is approximately:
\[
\text{The value of the car after three years is } \$24,980.00.
\]