Alexa bought a car for $\$ 18,000$. After 7 years, the car was worth $\$ 11,890$. If the depreciation was linear (straight-line depreciation method), what would the car be worth after 6 years? Round your answer to the nearest whole number. Your Answer: Answer

Step 1 ：Given that Alexa bought a car for $18,000 and after 7 years, the car was worth $11,890. The depreciation is linear, which means the car loses value at a constant rate each year.

Step 2 ：We can find this rate by subtracting the final value from the initial value and dividing by the number of years. The formula for this is \( \frac{{\text{{initial value}} - \text{{final value}}}}{{\text{{years}}}} \). Substituting the given values, we get \( \frac{{18000 - 11890}}{{7}} \approx 872.8571428571429 \). This is the depreciation rate per year.

Step 3 ：To find the value of the car after 6 years, we multiply the depreciation rate by 6 and subtract from the initial value. The formula for this is \( \text{{initial value}} - (\text{{depreciation rate}} \times \text{{years}}) \). Substituting the given values, we get \( 18000 - (872.8571428571429 \times 6) \approx 12762.857142857143 \).

Step 4 ：Rounding to the nearest whole number, the car would be worth approximately $12763 after 6 years.

Step 5 ：Final Answer: The car would be worth approximately \( \boxed{12763} \) dollars after 6 years.