To find the annual rate of change (depreciation) between 1990 and 2003, we can use the formula for annual rate of change in value, which is defined as:
\[ r = \frac{V_f - V_i}{V_i \cdot t} \]
Where:
- \(V_f\) = final value ($11,000 in 2003)
- \(V_i\) = initial value ($38,000 in 1990)
- \(t\) = number of years between 1990 and 2003 (which is 2003 - 1990 = 13 years)
Substituting the values into the formula:
\[ r = \frac{11000 - 38000}{38000 \cdot 13} \] \[ r = \frac{-27000}{494000} \] \[ r \approx -0.0546 \]
So the annual rate of change (depreciation) rounded to four decimal places is:
\[ r \approx -0.0546 \]
This means the car's value depreciated at an annual rate of approximately 5.46%.