https://file.aiquickdraw.com/mathbot/file/1727204420328khw2b5fi.jpg

The given function is:

\[
y = 51(0.91)^x
\]

### 1. Identifying Growth or Decay:
The function is of the form \( y = a(b)^x \), where \(a\) is the initial value and \(b\) is the growth/decay factor.

- If \(b > 1\), the function represents growth.
- If \(0 < b < 1\), the function represents decay.

In this case, \( b = 0.91 \), which is less than 1, so the function represents **exponential decay**.

### 2. Determining the Rate of Decrease:
The rate of decrease is given by \( (1 - b) \times 100 \% \).

\[
\text{Rate of decrease} = (1 - 0.91) \times 100 = 0.09 \times 100 = 9\%
\]

So, the percentage rate of decrease is **9%**.

Would you like more details or have any further questions?

Here are some related questions to deepen your understanding:
1. How would the function change if it represented exponential growth instead of decay?
2. What is the initial value in this function, and how does it affect the graph?
3. How can you determine the half-life of this function using the decay rate?
4. How would the function behave if the decay rate increased to 20%?
5. How do real-world problems model exponential decay, such as radioactive decay or depreciation?

**Tip:** Always check the value of the base \(b\) in an exponential function to easily identify if it represents growth or decay.

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease: y = 51(0.91)^x

Understand how to identify whether an exponential function represents growth or decay. Learn to calculate the percentage rate of increase or decrease using the function y = 51(0.91)^x. Perfect for students in Grades 9-12.

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