Question

These tables of values represent continuous functions. In which table do the values represent an exponential function?

A. X | Y
1. 7
2. 8
3. 9
4. 10
5. 11

B. X | Y
1. 10
2. 22
3. 34
4. 46
5. 58

C. X | Y
1. 2
2. 6
3. 18
4. 54
5. 162

D. X | Y
1. 3
2. 6
3. 9
4. 12
5. 15

Answer 1

To determine which table represents an exponential function, we need to look for a common characteristic of exponential functions: the ratio of successive values remains constant (indicating a constant multiplicative factor), or they grow at a consistent percentage rate.

Let's analyze the tables one by one:

**Table A:**
- The values are constant increments (1, 1, 1, 1). This is a linear function, not exponential.

**Table B:**
- The increments between successive y-values are:
- 22 - 10 = 12
- 34 - 22 = 12
- 46 - 34 = 12
- 58 - 46 = 12
- The differences are constant, which indicates a linear function, not exponential.

**Table C:**
- The values are:
- 6 / 2 = 3
- 18 / 6 = 3
- 54 / 18 = 3
- 162 / 54 = 3
- The ratio of each successive pair of y-values is constant and equal to 3. This indicates exponential growth. Therefore, this set of values represents an exponential function.

**Table D:**
- The increments between successive y-values are:
- 6 - 3 = 3
- 9 - 6 = 3
- 12 - 9 = 3
- 15 - 12 = 3
- The differences are constant, indicating a linear function, not exponential.

**Conclusion:**
The values in **Table C** represent an exponential function.