If an asset declines in value from $5000 to $ 3500 over nine years what is the mean annual growth rate in the asset's value over these nine years?

To calculate the mean annual growth rate (CAGR) of the asset's value, you can use the formula:

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

In this case, the beginning value is $5000, the ending value is $3500, and ( n ) is 9 years. Plugging in the values:

[ \text{CAGR} = \left( \frac{3500}{5000} \right)^{\frac{1}{9}} - 1 \approx -0.0955 \text{ or } -9.55% ]

Thus, the mean annual growth rate over the nine years is approximately -9.55%.