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.