Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y, equals, 340, left parenthesis, 0, point, 9, 0, 4, right parenthesis, to the power x
y=340(0.904) 
x

In the exponential function \( y = 340 \cdot (0.904)^x \), the base of the exponential term is 0.904, which is less than 1. This indicates that the function represents exponential **decay**.

To find the percentage rate of decay, use the following steps:

1. **Calculate the decay rate**:
   - The decay rate is given by \( 1 - 0.904 = 0.096 \).
   
2. **Convert to a percentage**:
   - Multiply by 100 to express this as a percentage: \( 0.096 \times 100 = 9.6\% \).

### Summary:
- **Type of Change**: Decay
- **Percentage Rate of Decay**: 9.6%

Would you like further explanation or have any questions?

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Here are some additional questions for practice:

1. What is the initial value of the function \( y = 340 \cdot (1.05)^x \)?
2. How would the function \( y = 340 \cdot (0.95)^x \) compare in terms of decay rate to \( y = 340 \cdot (0.904)^x \)?
3. If \( y = 340 \cdot (1.1)^x \), what would the percentage rate of growth be?
4. For the function \( y = 200 \cdot (0.75)^x \), what is the percentage rate of decay?
5. What effect does increasing the exponent \( x \) have on a decay function like \( y = 340 \cdot (0.904)^x \)?

**Tip:** For exponential functions of the form \( y = a \cdot (b)^x \), if \( b > 1 \), it’s growth; if \( 0 < b < 1 \), it’s decay.

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

 y = 340(0.904)^x

Determine if y = 340(0.904)^x represents exponential growth or decay, and calculate the percentage rate of decrease. This problem explores exponential functions, focusing on identifying decay and calculating decay rates, ideal for students in Grades 9-10.

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