Representing Functions Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
Use the table to answer the question.

Years, x Value of Car, f(x)

1 29, 750.00
2 25, 287.50
3 21, 494.38
4 18, 270.22
5 ?

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.

(1 point)
Rounded to the nearest cent, after 5 years, the value of the car will equal $
.
Remaining Attempts : 3
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Answer 1

To determine the value of the car after 5 years using the function \( f(x) = 35,000(0.85)^x \), we need to substitute \( x = 5 \) into the function.

Calculating \( f(5) \):

\[ f(5) = 35,000(0.85)^5 \]

First, calculate \( (0.85)^5 \):

\[ (0.85)^5 \approx 0.4437053125 \]

Now, multiply this by 35,000:

\[ f(5) = 35,000 \times 0.4437053125 \approx 15529.64859 \]

Rounding this to the nearest cent, the value of the car after 5 years is:

\[ f(5) \approx 15,529.65 \]

Thus, rounded to the nearest cent, after 5 years, the value of the car will equal $15,529.65.

Answer 2

To determine the value of the car after 5 years, substitute 5 into the function and evaluate.