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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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User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To find the value of the car after 5 years using the function \( f(x) = 35,000(0.85)^x \), substitute \( x = 5 \) into the equation:

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

Calculating \( (0.85)^5 \):

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

Now multiply by 35,000:

\[
f(5) = 35,000 \times 0.4437053125 \approx 15529.64659375
\]

Rounding this to the nearest cent gives:

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

Therefore, after 5 years, the value of the car will equal \(\$15,529.65\).