https://file.aiquickdraw.com/mathbot/file/1733986940368p0xt7a7u.jpg

From the provided image, we are tasked with determining whether the given exponential functions represent **exponential growth** or **exponential decay**.

### Key Idea:
- For exponential functions of the form \( f(x) = a^x \):
  - If \( a > 1 \), the function represents **exponential growth**.
  - If \( 0 < a < 1 \), the function represents **exponential decay**.

### Analyze Each Function:
1. **\( f(x) = 1.05^x \):**
   - The base is \( 1.05 \), which is greater than 1.
   - **This represents exponential growth.**

2. **\( f(x) = \left(\frac{2}{3}\right)^x \):**
   - The base is \( \frac{2}{3} \), which is less than 1 but greater than 0.
   - **This represents exponential decay.**

3. **\( f(x) = 0.99^x \):**
   - The base is \( 0.99 \), which is less than 1 but greater than 0.
   - **This represents exponential decay.**

### Final Answer:
1. \( f(x) = 1.05^x \): **Exponential Growth**
2. \( f(x) = \left(\frac{2}{3}\right)^x \): **Exponential Decay**
3. \( f(x) = 0.99^x \): **Exponential Decay**

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Would you like further explanation or examples?  

Here are 5 questions to consider:
1. How is exponential growth used in real-world problems like population modeling?
2. Why do exponential decay functions have values between 0 and 1?
3. Can we transform exponential functions into logarithmic forms?
4. How does the graph of exponential growth differ visually from decay?
5. What happens if the base is exactly 1 (e.g., \( f(x) = 1^x \))?

**Tip:** When analyzing exponential functions, always check the base \(a\) first to determine if it’s growth or decay!

Identify each function as representing exponential decay or exponential growth: f(x) = 1.05^x, f(x) = (2/3)^x, f(x) = 0.99^x.

Discover how to classify exponential functions like f(x) = 1.05^x, f(x) = (2/3)^x, and f(x) = 0.99^x as either growth or decay. Includes detailed step-by-step analysis, suitable for Grades 8-10 students studying algebra.

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