x

Question

y

0

4

1

12

2

36

3

108

4

324

Which of the following statements is true?

(1 point)

The initial value is 0.

The growth factor is 3.

The output doubles for every increase in the input.

The table represents linear growth.

Answer 1

To analyze the given data:

• \( x \) values: 0, 1, 2, 3, 4
• \( y \) values: 4, 12, 36, 108, 324

Now, let's evaluate the statements:

1. The initial value is 0.

   • The initial value \( y \) when \( x = 0 \) is \( 4 \), not \( 0 \). This statement is false.

2. The growth factor is 3.

   • Looking at the ratios of \( y \) values:
     • \( \frac{12}{4} = 3 \)
     • \( \frac{36}{12} = 3 \)
     • \( \frac{108}{36} = 3 \)
     • \( \frac{324}{108} = 3 \)
   • The growth factor between consecutive terms is consistently \( 3 \), so this statement is true.

3. The output doubles for every increase in the input.

   • The output does not double; it actually triples (e.g., \( 4 \) to \( 12 \) is a tripling, not doubling). This statement is false.

4. The table represents linear growth.

   • The growth between the \( y \) values is not uniform (the differences between \( y \) values increase). Since it grows by a factor of \( 3 \), it represents exponential, not linear growth. This statement is false.

The only true statement is "The growth factor is 3."