Question
1. 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.
Rounded to the nearest cent, after 5 years, the value of the car will equal $ ___.
Rounded to the nearest cent, after 5 years, the value of the car will equal $ ___.
Answers
GPT-4o mini
To determine the value of the car after 5 years using the function \( f(x) = 35,000(0.85)^x \), we will substitute \( x = 5 \) into the function.
\[
f(5) = 35,000(0.85)^5
\]
Now, let's calculate \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4437053125
\]
Next, we multiply this result by 35,000:
\[
f(5) = 35,000 \times 0.4437053125 \approx 15529.6759375
\]
Now, round to the nearest cent:
\[
f(5) \approx 15529.68
\]
Thus, rounded to the nearest cent, the value of the car after 5 years will equal **$15,529.68**.
\[
f(5) = 35,000(0.85)^5
\]
Now, let's calculate \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4437053125
\]
Next, we multiply this result by 35,000:
\[
f(5) = 35,000 \times 0.4437053125 \approx 15529.6759375
\]
Now, round to the nearest cent:
\[
f(5) \approx 15529.68
\]
Thus, rounded to the nearest cent, the value of the car after 5 years will equal **$15,529.68**.