To solve the equation for \( r \), we need to isolate \( r \) on one side. The given equation is:

\[
328 = 250 \times \left(1 + \frac{r}{100}\right)^5
\]

### Steps:

1. **Divide both sides by 250** to simplify the equation:
   \[
   \frac{328}{250} = \left(1 + \frac{r}{100}\right)^5
   \]
   \[
   1.312 = \left(1 + \frac{r}{100}\right)^5
   \]

2. **Take the fifth root** of both sides to remove the exponent:
   \[
   \sqrt[5]{1.312} = 1 + \frac{r}{100}
   \]

3. **Subtract 1** from both sides to isolate \(\frac{r}{100}\):
   \[
   \sqrt[5]{1.312} - 1 = \frac{r}{100}
   \]

4. **Multiply both sides by 100** to solve for \( r \):
   \[
   r = 100 \times \left(\sqrt[5]{1.312} - 1\right)
   \]

### Calculation:
Now, compute the value:

\[
\sqrt[5]{1.312} \approx 1.0557
\]
\[
r \approx 100 \times (1.0557 - 1) \approx 100 \times 0.0557 = 5.57\%
\]

So, the value of \( r \) is approximately **5.57%**.

Would you like to go over any details, or do you have any questions?

### Relative Questions:
1. How does compound interest influence the growth of investments?
2. What does the exponent in the equation represent in terms of financial growth?
3. Can you explain how the fifth root is related to the time period in this context?
4. How would the result change if the time period were different, say 10 years?
5. What is the significance of the percentage rate in financial calculations?

### Tip:
When dealing with exponentiation, remember that the exponent often represents time in financial equations, such as the number of periods in compound interest calculations.

Learn how to calculate compound interest growth using an exponential equation. Solve for the interest rate (r) in the compound interest formula with a detailed step-by-step solution. Suitable for high school students in Grades 10-12.

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