If an asset declines in value from $5,000 to $3,800 over nine years, what is the mean annual growth rate in the asset’s value over these nine years? Enter your answer as a percentage. If needed, round your answer to two decimal digits.

To find the mean annual growth rate of an asset that declines in value from \$5,000 to \$3,800 over nine years, you can use the formula for the compound annual growth rate (CAGR):

\[
\text{CAGR} = \left(\frac{\text{Final Value}}{\text{Initial Value}}\right)^{\frac{1}{n}} - 1
\]

Where:
- Final Value = \$3,800
- Initial Value = \$5,000
- $ n $ = 9 years

Let's calculate it:

\[
\text{CAGR} = \left(\frac{3800}{5000}\right)^{\frac{1}{9}} - 1
\]

First, compute the ratio:

\[
\frac{3800}{5000} = 0.76
\]

Then, raise this ratio to the power of $\frac{1}{9}$:

\[
0.76^{\frac{1}{9}} \approx 0.9715
\]

Finally, subtract 1 and convert to a percentage:

\[
\text{CAGR} = (0.9715 - 1) \times 100 \approx -2.85\%
\]

So, the mean annual growth rate is approximately **-2.85%**.

Would you like more details or have any questions? Here are some related questions:

1. How is the compound annual growth rate different from the simple average rate of change?
2. What is the significance of a negative growth rate?
3. How would the CAGR change if the time period was longer?
4. Can CAGR be used for assets with non-linear growth?
5. How do you interpret a CAGR value in financial analysis?

**Tip:** CAGR is particularly useful for comparing the growth of different investments or assets over time.

Find the mean annual growth rate of an asset that declines from $5,000 to $3,800 over nine years. This guide explains the Compound Annual Growth Rate (CAGR) formula and provides a step-by-step solution. Suitable for advanced high school and college students.

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