Question

Consider the table of values: y 0 4 1 12 2 36 3 108 4 324 Which of the following is a true statement? The output doubles for every increase in the input. The growth factor is 3. The initial value is 0. The growth factor is 4.

Answer 1

To analyze the table of values provided:

- Input (x) = 0, Output (y) = 0
- Input (x) = 1, Output (y) = 4
- Input (x) = 2, Output (y) = 12
- Input (x) = 3, Output (y) = 108
- Input (x) = 4, Output (y) = 324

Now, let's check each of the provided statements:

1. **The output doubles for every increase in the input.**
- Checking outputs:
- From 0 to 1: 0 → 4 (not doubling)
- From 1 to 2: 4 → 12 (not doubling)
- From 2 to 3: 12 → 108 (not doubling)
- From 3 to 4: 108 → 324 (not doubling)
- This statement is false.

2. **The growth factor is 3.**
- Checking the ratios between successive outputs:
- 4 / 0 is undefined.
- 12 / 4 = 3
- 108 / 12 = 9
- 324 / 108 = 3
- The growth factor is not consistent (it’s 3 for some pairs but not all). This statement is false.

3. **The initial value is 0.**
- The initial value when x = 0 is y = 0.
- This statement is true.

4. **The growth factor is 4.**
- As calculated previously, the growth factor varies and is not consistently 4. This statement is false.

Among the statements, the true statement is:
**The initial value is 0.**