\[
r = \left( \frac{147,332}{20,500} \right)^{\frac{1}{17}} - 1
\]


Let's break down the given equation to solve for \( r \).

The expression is:

\[
r = \left( \frac{147,332}{20,500} \right)^{\frac{1}{17}} - 1
\]

1. First, compute the fraction:

\[
\frac{147,332}{20,500} \approx 7.186
\]

2. Next, take the 17th root of this value:

\[
7.186^{\frac{1}{17}} \approx 1.127
\]

3. Finally, subtract 1:

\[
r = 1.127 - 1 = 0.127
\]

So, \( r \approx 0.127 \) or 12.7%.

Let me know if you'd like further details or have any questions!

Here are 5 related questions:
1. How is the 17th root calculated in this context?
2. What is the significance of the \( r \) value in financial or growth contexts?
3. How does changing the fraction values affect \( r \)?
4. What if the exponent were different, say \( \frac{1}{10} \) instead of \( \frac{1}{17} \)?
5. Can this formula be related to compound interest problems?

**Tip:** In growth models, the rate \( r \) typically represents the percentage growth per period.

r = \left( \frac{147,332}{20,500} \right)^{\frac{1}{17}} - 1

Learn how to calculate the growth rate using the formula r = (147,332 / 20,500)^(1/17) - 1, with step-by-step explanations. This problem involves exponentiation, n-th root extraction, and is suitable for high school students in Grades 10-12.

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