Use the table to answer the question.

Question

Years, x Value of Car, f(x)
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
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 $

Answer 1

To find the value of the car after 5 years using the given function $f(x)=35,000(0.85{)}^x$, we need to substitute $x=5$ into the equation.

$$f(5)=35,000(0.85{)}^5$$

First, we calculate $(0.85{)}^5$:

$$(0.85{)}^5\approx 0.4437$$

Now substitute this value back into the function:

$$f(5)=35,000\times 0.4437\approx 15,034.50$$

Thus, the value of the car after 5 years, rounded to the nearest cent, is:

$$\boxed{{\displaystyle 15034.50}}$$