The image contains a multiple-choice question about the difference between exponential growth and exponential decay. Here's a breakdown of the options:

1. The base for exponential growth is always a number smaller than 1 while the base for exponential decay is always a number larger than 1.

   • This statement is incorrect. In exponential growth, the base is greater than 1, and for exponential decay, the base is between 0 and 1.

2. For exponential growth represented by a table, the y-values increase as the x-values increase. For exponential decay represented by a table, the y-values decrease as the x-values increase.

   • This statement is correct. In exponential growth, as the x-values (typically time or another independent variable) increase, the y-values increase. For exponential decay, as the x-values increase, the y-values decrease.

3. The graph for exponential growth decreases while the graph of exponential decay increases.

   • This statement is incorrect. The graph of exponential growth increases, while the graph of exponential decay decreases.

4. The formula for exponential growth is y = a(1 - r)^x while the formula for exponential decay is y = a(1 + r)^x.

   • This statement is incorrect. The correct formula for exponential growth is y = a(1 + r)^x, and the formula for exponential decay is y = a(1 - r)^x.

The best answer to this question is:
"For exponential growth represented by a table, the y-values increase as the x-values increase. For exponential decay represented by a table, the y-values decrease as the x-values increase."

Let me know if you need further clarification or have additional questions!

Follow-up questions:

1. What is the general form of the exponential growth and decay formulas?
2. How can you identify exponential growth or decay just by looking at a graph?
3. What are real-life applications of exponential growth and decay?
4. How do exponential functions compare to linear functions in graphs?
5. What happens if the base in an exponential function is exactly 1?

Tip: When analyzing exponential functions, remember that a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay!