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. Find the value of the car to the cent after three years
Answers
GPT-4o mini
To find the value of the car after three years, we can use the provided function:
\[ f(x) = 32,000(0.92)^x \]
We need to substitute \( x = 3 \) into the equation to find \( f(3) \):
\[ f(3) = 32,000(0.92)^3 \]
First, we calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now, we can multiply this value by $32,000:
\[
f(3) = 32,000 \times 0.778688
\]
Calculating the above:
\[
f(3) \approx 24,996.00
\]
Thus, the value of the car after three years is approximately **$24,996.00** (to the cent).
\[ f(x) = 32,000(0.92)^x \]
We need to substitute \( x = 3 \) into the equation to find \( f(3) \):
\[ f(3) = 32,000(0.92)^3 \]
First, we calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now, we can multiply this value by $32,000:
\[
f(3) = 32,000 \times 0.778688
\]
Calculating the above:
\[
f(3) \approx 24,996.00
\]
Thus, the value of the car after three years is approximately **$24,996.00** (to the cent).