Question

A car was valued at $38,000 in the year 1990. The value depreciated to $11,000 by the year 2003.

A) What was the annual rate of change between 1990 and 2003?
r
r = Round the rate of decrease to 4 decimal places.

Answer 1

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%.