Calculate the compound growth rate given the following annual growth rates.

Note: Round your intermediate calculations at least to 4 decimal places and final answer to 2 decimal places.

4.50%	5.60%	3.80%	4.20%	7.20%

To calculate the compound growth rate (also known as the geometric average growth rate), we use the formula:

\[
CAGR = \left( \prod_{i=1}^{n} (1 + r_i) \right)^{\frac{1}{n}} - 1
\]

Where:
- \( r_i \) are the individual growth rates for each year (expressed as decimals),
- \( n \) is the number of growth rates.

For the growth rates provided:
- 4.50% → 0.045
- 5.60% → 0.056
- 3.80% → 0.038
- 4.20% → 0.042
- 7.20% → 0.072

### Step-by-step solution:

1. Convert each percentage to a decimal and add 1:
   \[
   1.045, 1.056, 1.038, 1.042, 1.072
   \]

2. Multiply these values together:
   \[
   \text{Product} = 1.045 \times 1.056 \times 1.038 \times 1.042 \times 1.072
   \]

3. Take the 5th root of the product (since there are 5 growth rates) and subtract 1 to find the compound growth rate.

Let me calculate that for you.The compound growth rate is approximately **5.05%**.

Would you like any additional details or clarifications? Here are some related questions to explore:

1. How does compound growth differ from simple growth?
2. What impact does a negative growth rate have on compound growth?
3. How would the compound growth rate change if there were more years of growth data?
4. What real-world applications use compound growth calculations?
5. How can we apply the compound growth rate formula to financial investments?

**Tip:** When dealing with growth rates over time, always remember to use the geometric average for accuracy, especially if the rates vary significantly.

Calculate the compound growth rate given the following annual growth rates: 4.50%, 5.60%, 3.80%, 4.20%, 7.20%. Note: Round your intermediate calculations at least to 4 decimal places and final answer to 2 decimal places.

Learn how to calculate the compound growth rate using the geometric average for the following annual growth rates: 4.50%, 5.60%, 3.80%, 4.20%, and 7.20%. This step-by-step guide includes formula application and final calculations. Suitable for Grades 11-12 and college-level students.

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