We have the equation:

\[
147,332 = 20,500 \times (1 + r)^{17}
\]

To solve for \(r\), we can follow these steps:

### Step 1: Divide both sides by 20,500 to isolate \((1 + r)^{17}\):

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

\[
7.1879 = (1 + r)^{17}
\]

### Step 2: Take the 17th root of both sides to eliminate the exponent:

\[
(7.1879)^{\frac{1}{17}} = 1 + r
\]

### Step 3: Calculate the 17th root of 7.1879:

\[
(7.1879)^{\frac{1}{17}} \approx 1.1099
\]

### Step 4: Subtract 1 from both sides to solve for \(r\):

\[
1.1099 - 1 = r
\]

\[
r \approx 0.1099
\]

### Final Answer:
The value of \(r\) is approximately **0.1099** or **10.99%**.

Would you like more details or explanations on any step?

Here are 5 related questions you might find interesting:
1. How do you solve equations involving compound interest?
2. What is the significance of the 17th root in this problem?
3. How does the value of \(r\) affect long-term growth in compound interest problems?
4. What is the difference between continuous and periodic compounding?
5. How do logarithms help in solving exponential equations?

**Tip:** When solving exponential equations, taking roots or using logarithms is often the key to isolating the variable.

Learn how to solve the exponential equation 147,332 = 20,500(1 + r)^17 to find the interest rate r. This problem involves key concepts like compound interest, exponentiation, and root extraction. Suitable for students in Grades 10-12, this step-by-step guide breaks down the solution process.

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