$1.43

1.57

1.72

1.88                                      
Compute the average historical growth rate.

To calculate the average historical growth rate, we use the **geometric mean growth rate** formula, which is ideal for a series of growth rates. Here's the step-by-step process:

1. **Calculate individual growth rates** between consecutive values:

   - Growth rate from 1.43 to 1.57:
     \[
     \frac{1.57 - 1.43}{1.43} = \frac{0.14}{1.43} \approx 0.0979 \text{ or } 9.79\%
     \]
   
   - Growth rate from 1.57 to 1.72:
     \[
     \frac{1.72 - 1.57}{1.57} = \frac{0.15}{1.57} \approx 0.0955 \text{ or } 9.55\%
     \]
   
   - Growth rate from 1.72 to 1.88:
     \[
     \frac{1.88 - 1.72}{1.72} = \frac{0.16}{1.72} \approx 0.0930 \text{ or } 9.30\%
     \]

2. **Find the geometric mean** of the growth rates:
   
   Use the formula for the geometric mean:
   \[
   \text{Geometric Mean} = \left( (1 + 0.0979) \times (1 + 0.0955) \times (1 + 0.0930) \right)^{\frac{1}{3}} - 1
   \]

   Let's compute this value.

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Would you like to continue with any other calculations or queries? 

Here are some related questions you may find useful:
1. How do you calculate the arithmetic average growth rate?
2. What is the difference between arithmetic and geometric mean in growth rates?
3. How do compound growth rates work for financial projections?
4. What if one of the values in the growth rate series is negative?
5. How do you interpret historical growth rates in economic data?

**Tip:** The geometric mean is the preferred method for averaging growth rates over multiple periods because it accounts for the compounding effect.

Compute the average historical growth rate for the values 1.43, 1.57, 1.72, 1.88.

This page explains how to compute the average historical growth rate using the geometric mean formula, with a detailed example based on the values 1.43, 1.57, 1.72, and 1.88. Learn the step-by-step process and key formulas. Suitable for high school students (Grades 10-12).

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