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 $.
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 using the given equation \( f(x) = 32,000(0.92)^x \), we can plug in \( x = 3 \):
\[
f(3) = 32,000(0.92)^3
\]
First, calculate \( (0.92)^3 \):
\[
0.92^3 = 0.778688
\]
Now multiply this by $32,000:
\[
f(3) = 32,000 \times 0.778688 \approx 24,971.00
\]
Thus, the value of the car after three years is approximately:
\[
\text{Value of the car after three years} = \$24,971.00
\]
So, the value of the car after three years is **$24,971.00**.
\[
f(3) = 32,000(0.92)^3
\]
First, calculate \( (0.92)^3 \):
\[
0.92^3 = 0.778688
\]
Now multiply this by $32,000:
\[
f(3) = 32,000 \times 0.778688 \approx 24,971.00
\]
Thus, the value of the car after three years is approximately:
\[
\text{Value of the car after three years} = \$24,971.00
\]
So, the value of the car after three years is **$24,971.00**.