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 $
1 answer
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:
\[ \boxed{15034.50} \]
