A. Write G on the blank if the given exponential function exhibits growth and D if decay. (10 points)

1. y = 4 ^ x

2. f(x) = (1/2) ^ x

3. y = 3 ^ x

4. g(x) = (1/4) ^ x

5. y = 2 (2) ^ x

6. y = 5 ^ x

7. h(x) = (4/5) ^ x

8. g(x) = (4/5) ^ - x

9. h(x) = (2/3) ^ x

10. y = 6 ^ x

To determine if the exponential functions represent growth or decay, we check the base of the exponential expression:

- If the base is greater than 1, the function exhibits **growth**.
- If the base is between 0 and 1, the function exhibits **decay**.

### Let's go through each one:

1. \( y = 4^x \)  
   Base \( 4 > 1 \), so it's **Growth (G)**.

2. \( f(x) = \left( \frac{1}{2} \right)^x \)  
   Base \( \frac{1}{2} < 1 \), so it's **Decay (D)**.

3. \( y = 3^x \)  
   Base \( 3 > 1 \), so it's **Growth (G)**.

4. \( g(x) = \left( \frac{1}{4} \right)^x \)  
   Base \( \frac{1}{4} < 1 \), so it's **Decay (D)**.

5. \( y = 2(2^x) \)  
   The exponential part \( 2^x \) has base \( 2 > 1 \), so it's **Growth (G)**.

6. \( y = 5^x \)  
   Base \( 5 > 1 \), so it's **Growth (G)**.

7. \( h(x) = \left( \frac{4}{5} \right)^x \)  
   Base \( \frac{4}{5} < 1 \), so it's **Decay (D)**.

8. \( g(x) = \left( \frac{4}{5} \right)^{-x} \)  
   Since \( -x \) reverses the base behavior, it's equivalent to \( \left( \frac{5}{4} \right)^x \), and \( \frac{5}{4} > 1 \), so it's **Growth (G)**.

9. \( h(x) = \left( \frac{2}{3} \right)^x \)  
   Base \( \frac{2}{3} < 1 \), so it's **Decay (D)**.

10. \( y = 6^x \)  
    Base \( 6 > 1 \), so it's **Growth (G)**.

### Final Answers:
1. **G**
2. **D**
3. **G**
4. **D**
5. **G**
6. **G**
7. **D**
8. **G**
9. **D**
10. **G**

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Would you like more details on any of these? Here are 5 follow-up questions you could explore:

1. How does the negative exponent affect the growth or decay of a function?
2. What are some real-world examples of exponential growth and decay?
3. How does adding a constant factor (like in \( 2(2^x) \)) affect the behavior of an exponential function?
4. Can an exponential decay function ever become negative?
5. How do exponential functions compare to linear or quadratic functions in terms of growth rate?

**Tip:** In any exponential function, the base value determines whether it grows or decays, regardless of any constants multiplied out front.

A. Write G on the blank if the given exponential function exhibits growth and D if decay. (10 points)
1. y = 4 ^ x
2. f(x) = (1/2) ^ x
3. y = 3 ^ x
4. g(x) = (1/4) ^ x
5. y = 2 (2) ^ x
6. y = 5 ^ x
7. h(x) = (4/5) ^ x
8. g(x) = (4/5) ^ - x
9. h(x) = (2/3) ^ x
10. y = 6 ^ x

Learn how to determine if exponential functions exhibit growth or decay based on their base values. Includes examples such as y = 4^x, f(x) = (1/2)^x, and y = 5^x. Suitable for students in Grades 9-12.

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