Question

Which equation represents exponential growth? (1 point) Responses f(x)=2(3)x f x = 2 3 x f(x)=3(0.11)x f x = 3 0 . 11 x f(x)=2(12)x f x = 2 1 2 x f(x)=5(16x)

Answer 1

To determine which equation represents exponential growth, we need to look for a function of the form \( f(x) = a(b^x) \) where \( a > 0 \) and \( b > 1 \).

Let's analyze each option:

1. **\( f(x) = 2(3)^x \)**: Here, \( a = 2 \) (which is positive) and \( b = 3 \) (which is greater than 1). This represents exponential growth.

2. **\( f(x) = 3(0.11)^x \)**: Here, \( a = 3 \) (positive) and \( b = 0.11 \) (less than 1). This represents exponential decay.

3. **\( f(x) = 2(12)^x \)**: Here, \( a = 2 \) (positive) and \( b = 12 \) (greater than 1). This also represents exponential growth.

4. **\( f(x) = 5(16x) \)**: This expression is not in the form of exponential growth; it is linear due to the multiplication by \( x \).

Based on this analysis, the equations that represent exponential growth are:
- \( f(x) = 2(3)^x \)
- \( f(x) = 2(12)^x \)

If you can choose only one, **\( f(x) = 2(3)^x \)** is a valid response for exponential growth.