Question

an automobile purchased for $29,000 is worth $2400 after 7 years. assuming that the car’s value depreciated steadily from year to year, what was it worth at the end of the third year? the value 3 years after it was purchased is $\square$.

Explanation:

Step1: Find the depreciation rate per year

The initial value \( V_0 = 29000 \), value after 7 years \( V_7 = 2400 \). The depreciation is linear, so the slope (depreciation per year) \( m=\frac{V_7 - V_0}{7 - 0}=\frac{2400 - 29000}{7}=\frac{-26600}{7}=-3800 \).

Step2: Find the value at 3 years

Using the linear equation \( V(t)=V_0+mt \), substitute \( t = 3 \), \( V_0 = 29000 \), \( m=-3800 \). So \( V(3)=29000+(-3800)\times3=29000 - 11400 = 17600 \).

Answer:

17600