Question

The value of a certain car, in dollar, x years from its model year can be predicted by the following function:f(x)=17,000(0.87)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.
x | 0| 1| 2| 3| 4| 5|
g(x)| 21,000| 18,690| 16,634.10| 14,804.35| 13,175.87| 11,726.52|
How much more will the SUV be worth than the car 5 years after their model years? Round your answer to the nearest cent.

Answer 1

After 5 years, the SUV will be worth $3,255.08 more than the car. This is determined by evaluating the depreciation functions for both vehicles for x=5 and subtracting the car's value from the SUV's value.

Step-by-step explanation:

The problem asks us to compare the values of a car and an SUV five years after their model years using their respective depreciation functions. The car's value is given by the function f(x) = 17,000(0.87)x and the SUV's value is provided in tabular form. To find the car's value after 5 years, we plug in x=5 into the car's depreciation function.

f(5) = 17,000(0.87)5 = 17,000(0.49832) ≈ $8,471.44

We are given that the SUV's value after 5 years is $11,726.52. To find how much more the SUV is worth than the car after 5 years, we subtract the car's value from the SUV's value.

Value difference = SUV's value - Car's value = $11,726.52 - $8,471.44 = $3,255.08

Therefore, the SUV will be worth $3,255.08 more than the car five years after their model years. This value is rounded to the nearest cent.