Question

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the value of a certain car, in dollars, x years from its model year can be predicted by the function f(x) = 12,000(0.89)^x.
the value of a certain suv, in dollars, x years from its model year can be predicted by the exponential function shown in the table.
how much more will the suv be worth than the car 5 years after their model years?
enter your answer, rounded to the nearest cent, in the box.
$

x	g(x)
1	14,280
2	11,995
3	10,076
4	8463.81
5	7109.60

Explanation:

Step1: Calculate car's value at x=5

Use the function \( f(x) = 12000(0.89)^x \). Substitute \( x = 5 \):
\( f(5) = 12000(0.89)^5 \). Calculate \( (0.89)^5 \approx 0.5584 \), so \( f(5) \approx 12000 \times 0.5584 = 6700.8 \).

Step2: Find SUV's value at x=5

From the table, when \( x = 5 \), \( g(5) = 7109.60 \).

Step3: Compute the difference

Subtract car's value from SUV's value: \( 7109.60 - 6700.8 = 408.8 \).

Answer:

\( 408.80 \)