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.