1. The problem is to understand the average growth factor over 6 years using the geometric mean, which Bob calculated as 1.24.
2. The geometric mean $G$ of $n$ growth factors $g_1, g_2, \ldots, g_n$ is given by:
$$G = \sqrt[n]{g_1 \times g_2 \times \cdots \times g_n}$$
3. Here, $n=6$ and $G=1.24$, so:
$$1.24 = \sqrt[6]{g_1 \times g_2 \times g_3 \times g_4 \times g_5 \times g_6}$$
4. To find the product of the individual growth factors, raise both sides to the 6th power:
$$g_1 \times g_2 \times g_3 \times g_4 \times g_5 \times g_6 = 1.24^6$$
5. Calculate $1.24^6$:
$$1.24^6 \approx 3.82$$
6. This means the total growth factor over 6 years is approximately 3.82, indicating the store's size multiplied by about 3.82 times over the period.
7. The average annual growth factor is 1.24, meaning on average, the store grew by 24% each year compounded.
Final answer: The product of the individual growth factors over 6 years is approximately 3.82, and the average annual growth factor is 1.24.
Average Growth Factor
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