Question
A car decreases in value after a given number of years. The following function represents the value of the car in dollars with respect to its age, x, in years: f(x) = 35,000(.85)^x. Use the input-output table to determine the value of the car after 5 years. Round your answer to the nearest cent.
Answers
GPT-4o mini
To find the value of the car after 5 years using the function \( f(x) = 35,000(0.85)^x \), we'll substitute \( x = 5 \) into the function.
\[
f(5) = 35,000(0.85)^5
\]
First, we need to calculate \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4437053125
\]
Now we can substitute this value back into the function:
\[
f(5) = 35,000 \times 0.4437053125
\]
Calculating this:
\[
f(5) \approx 35,000 \times 0.4437053125 \approx 15529.64
\]
Thus, the value of the car after 5 years is approximately **$15,529.64** when rounded to the nearest cent.
\[
f(5) = 35,000(0.85)^5
\]
First, we need to calculate \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4437053125
\]
Now we can substitute this value back into the function:
\[
f(5) = 35,000 \times 0.4437053125
\]
Calculating this:
\[
f(5) \approx 35,000 \times 0.4437053125 \approx 15529.64
\]
Thus, the value of the car after 5 years is approximately **$15,529.64** when rounded to the nearest cent.
that's wrong