The question asks which table represents an exponential function. Let's analyze the tables:

An exponential function grows by a constant multiplicative factor rather than a constant additive factor. In an exponential function, for example $y = a \cdot b^x$, $b$ is a constant multiplier.

Let's go through the options:

• Table A:

  • $x = 0, 1, 2, 3, 4$
  • $y = 5, 6, 7, 8, 9$

  Here, $y$ increases by a constant amount (1), so this is linear, not exponential.

• Table B:

  • $x = 0, 1, 2, 3, 4$
  • $y = 22, 44, 66, 88, 110$

  Here, $y$ increases by adding 22, so this is also linear, not exponential.

• Table C:

  • $x = 0, 1, 2, 3, 4$
  • $y = 1, 2, 4, 8, 16$

  Here, $y$ is doubling each time, meaning the factor is multiplying by 2. This is exponential.

• Table D:

  • $x = 0, 1, 2, 3, 4$
  • $y = 3, 9, 27, 81, 243$

  Here, $y$ is multiplying by 3 each time. This is also an exponential function.

Conclusion:

Both Table C and Table D represent exponential functions, but the most commonly used answer for a basic exponential form $y = a \cdot 2^x$ would be Table C, where the multiplication factor is 2.

Would you like more details on how to spot exponential functions or further explanations?

Relative Questions:

1. What is the difference between exponential and linear functions?
2. How can you tell if a table of values represents a quadratic function?
3. What happens to the graph of an exponential function when the base is greater than 1?
4. Can exponential functions ever decrease, and how does that work?
5. How can exponential growth models apply to real-world problems?

Tip:

Exponential functions grow much faster than linear or quadratic functions because they multiply by a constant factor rather than adding a constant amount.