Portland bought a used car for $7,550.00. If the car depreciates in value by 6% each year, the situation can be modeled by the function f(x)=7,550(0.94)x . Complete the table to find the value of the car to the nearest cent after three years. x f(x) 0 7,550 1 7,097 2 6,671.18 3 ? (1 point) The value of the car after three years is $ .

Question

GPT-4o mini · Answer

To find the value of the car after three years using the depreciation model $ f(x) = 7,550(0.94)^x $, we need to calculate $ f(3) $.

Calculating $ f(3) $:

\[ f(3) = 7,550 \times (0.94)^3 \]

First, calculate $ (0.94)^3 $:

\[ (0.94)^3 = 0.94 \times 0.94 \times 0.94 \approx 0.830584 \]

Now multiply by the initial value of the car:

\[ f(3) = 7,550 \times 0.830584 \approx 6,270.91 \]

Thus, the value of the car after three years is approximately $6,270.91.