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 equation f(x)=32,000(0.92)x (1 point) The value of the car after three years is $ (to the nearest cent). Question 2
Answers
GPT-4o mini
To find the value of the car after three years using the given depreciation model, we can substitute \( x = 3 \) into the equation:
\[
f(x) = 32,000(0.92)^x
\]
Substituting \( x = 3 \):
\[
f(3) = 32,000(0.92)^3
\]
Calculating \( (0.92)^3 \):
\[
0.92^3 \approx 0.778688
\]
Now, multiplying this by 32,000:
\[
f(3) = 32,000 \times 0.778688 \approx 24,996.00
\]
Thus, the value of the car after three years is approximately **$24,996.00** (to the nearest cent).
\[
f(x) = 32,000(0.92)^x
\]
Substituting \( x = 3 \):
\[
f(3) = 32,000(0.92)^3
\]
Calculating \( (0.92)^3 \):
\[
0.92^3 \approx 0.778688
\]
Now, multiplying this by 32,000:
\[
f(3) = 32,000 \times 0.778688 \approx 24,996.00
\]
Thus, the value of the car after three years is approximately **$24,996.00** (to the nearest cent).