Linear vs. Exponential Growth Rates Practice

To answer your question regarding the growth rates of Function #1 (linear) and Function #2 (exponential), we can analyze how growth behaves for each type of function.

### Key Characteristics:

1. **Linear Growth (Function #1)**: A linear function has a constant rate of change. This means that as x increases, the value of the function increases by a fixed amount for each unit increase in x.

2. **Exponential Growth (Function #2)**: An exponential function grows at a rate proportional to its current value. This means that as x increases, the value of the function increases by an ever-larger amount.

### Growth Comparison:

- **Initially**: At the beginning (for smaller values of x), linear functions typically have a greater or comparable growth rate because the exponential growth rate hasn't had enough time to significantly outpace the linear growth.

- **By x=8**: At this point, exponential growth typically begins to surpass linear growth. This is because the nature of exponential growth leads to rapid increases once the base of the exponent (the rate of growth) compounds enough.

### Conclusion Statement:

Based on the typical behavior of linear and exponential functions, you can fill in the blanks in your original question as follows:

- Initially, Function #1 (linear) has the greater growth rate. By x=8, the growth rate of Function #2 (exponential) surpasses the growth rate of Function #1 (linear).

This description aligns with the characteristics of linear versus exponential growth rates. If you have any specific values or additional context from the image, I can help refine the analysis further!