david electronics had a profit of $10 million in 2002. Profit doubled from 2002 to 2003 and profit increased eight fold from 2003 to 2004. what was the annual geometric mean rate of growth from 2002 to 2004?

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To find the annual geometric mean rate of growth from 2002 to 2004, we need to calculate the total growth and then convert it to an annual average growth rate.

First, let's calculate the profit for each year:

Profit in 2002 = $10 million
Profit in 2003 = $10 million doubled = $10 million * 2 = $20 million
Profit in 2004 = $20 million increased eight-fold = $20 million * 8 = $160 million

Next, we'll calculate the total growth from 2002 to 2004:

Total growth = Profit in 2004 - Profit in 2002
Total growth = $160 million - $10 million = $150 million

Now, we'll calculate the annual average growth rate using the formula for the geometric mean rate of growth:

Annual average growth rate = (Total growth)^(1/Number of years) - 1

Number of years = 2004 - 2002 = 2 years

Substituting the values into the formula, we get:

Annual average growth rate = ($150 million)^(1/2) - 1

Calculating this expression, we find:

Annual average growth rate ≈ 11.80

Therefore, the annual geometric mean rate of growth from 2002 to 2004 is approximately 11.80%.