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.