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In the given exponential function \( y = 25(1.071)^x \), we can identify whether it represents growth or decay by examining the base of the exponent, which is \( 1.071 \) here.

### Step-by-Step Solution

1. **Identify Growth or Decay**:
   - Since the base \( 1.071 \) is greater than 1, this indicates **growth**.

2. **Determine the Percentage Rate**:
   - The growth rate is found by subtracting 1 from the base: \( 1.071 - 1 = 0.071 \).
   - To express this as a percentage, multiply by 100: \( 0.071 \times 100 = 7.1\% \).

### Conclusion
- This function represents **growth** with a **7.1% increase**.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the function change if it represented a decay instead of growth?
2. What would the base need to be for a decay rate of 5%?
3. Can you find the growth rate if the base of the exponent was \(1.05\)?
4. How does changing the coefficient (like 25) affect the function's growth rate?
5. What happens to the function’s growth rate if the base is exactly 1?

**Tip:** For exponential functions, bases greater than 1 indicate growth, while bases between 0 and 1 indicate decay.

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease: y = 25(1.071)^x.

Learn how to determine if an exponential function, such as y = 25(1.071)^x, represents growth or decay and calculate the percentage rate. This math problem covers exponential growth concepts and is ideal for Grades 8-10.

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