## Question:

The geometric mean is often used in business and economics for finding average rates of change, average rates of growth, or average ratios. Given n scores (all of which are positive), the geometric mean is the «th root of their product. For example, the geometric mean of 2, 4, and 10 is found by first multiplying the scores to get 80, then taking the cube root (because there are 3 scores) of the product to get 4.3. The average growth factor for money compounded at annual interest rates of 10%, 8%, 9%, 12%, and 7% can be found by computing the geometric mean of the growth factors 1.10, 1.08, 1.09, 1.12, and 1.07. Find that average growth factor.