Question
Use the table to answer the question. x f(x) 0 32,000 1 29,440 2 27,048.80 3 ? 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 equation 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 $
Answers
GPT-4o mini
To find the value of the car after three years, we can use the provided equation for depreciation:
\( f(x) = 32,000(0.92)^x \)
where \( x \) is the number of years since the purchase.
For \( x = 3 \):
\[
f(3) = 32,000(0.92)^3
\]
First, we need to calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now, substituting this value back into the equation:
\[
f(3) = 32,000 \times 0.778688
\]
\[
f(3) \approx 24,996.00
\]
Thus, rounding to the nearest cent, the value of the car after three years is approximately:
\[
\text{The value of the car after three years is } \$24,996.00.
\]
\( f(x) = 32,000(0.92)^x \)
where \( x \) is the number of years since the purchase.
For \( x = 3 \):
\[
f(3) = 32,000(0.92)^3
\]
First, we need to calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now, substituting this value back into the equation:
\[
f(3) = 32,000 \times 0.778688
\]
\[
f(3) \approx 24,996.00
\]
Thus, rounding to the nearest cent, the value of the car after three years is approximately:
\[
\text{The value of the car after three years is } \$24,996.00.
\]