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 values (all of which are positive), the geometric mean Is the nth root of their product. The average growth factor for money compounded at annual interest rates of 14.4% ,7.3% and 2.4% can be found by computing the geometric mean of 1.144,1.073 and 1.024. Find that average growth factor.or geometric mean. What single percentage growth rate would be the same as having three successive growth rates of 14.4% ,7.3% and 2.4% Is that result the same as the mean of 14.4% ,7.3% and 24% The average growth factor.or geometric mean, is square (Round to four decimal places as needed.)

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 values (all of which are positive), the geometric mean Is the nth root of their product. The average growth factor for money compounded at annual interest rates of 14.4% ,7.3% and 2.4% can be found by computing the geometric mean of 1.144,1.073 and 1.024. Find that average growth factor.or geometric mean. What single percentage growth rate would be the same as having three successive growth rates of 14.4% ,7.3% and 2.4% Is that result the same as the mean of 14.4% ,7.3% and 24% The average growth factor.or geometric mean, is square (Round to four decimal places as needed.)

Answer 1

To find the geometric mean of the given values, we need to compute the nth root of their product.Given values: 1.144, 1.073, and 1.024Step 1: Compute the product of the given values.Product = 1.144 * 1.073 * 1.024 = 1.244928Step 2: Compute the geometric mean by taking the cube root (since there are three values) of the product.Geometric Mean = (1.244928)^(1/3) ≈ 1.0800Therefore, the average growth factor, or geometric mean, is approximately 1.0800.To find the single percentage growth rate that would be the same as having three successive growth rates of 14.4%, 7.3%, and 2.4%, we need to find the geometric mean of the given percentages.Given percentages: 14.4%, 7.3%, and 2.4%Step 1: Convert the percentages to their decimal form.14.4% = 0.1447.3% = 0.0732.4% = 0.024Step 2: Compute the product of the decimal values.Product = 0.144 * 0.073 * 0.024 = 0.025152Step 3: Compute the geometric mean by taking the cube root (since there are three values) of the product.Geometric Mean = (0.025152)^(1/3) ≈ 0.2800Step 4: Convert the geometric mean back to a percentage.Geometric Mean Percentage = 0.2800 * 100% = 28.00%Therefore, the single percentage growth rate that would be the same as having three successive growth rates of 14.4%, 7.3%, and 2.4% is approximately 28.00%.The result is not the same as the mean of 14.4%, 7.3%, and 24%. The mean of these percentages would be (14.4% + 7.3% + 24%) / 3 = 15.03%, which is different from the geometric mean of 28.00%.

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