Question

Which equation represents exponential growth?

answers below:

f (z) = 2 (3)^x
f (z) = 3 (0.11)^x
f (z) = 2 (1/2)^x
f (z) = 5 (1/6^x)

Answer 1

Exponential growth occurs when a function increases as the input increases, typically represented by a base greater than 1.

Let's analyze the provided equations:

1. **f(z) = 2 (3)^x**: Here, the base is 3, which is greater than 1. This represents exponential growth.

2. **f(z) = 3 (0.11)^x**: The base is 0.11, which is less than 1. This represents exponential decay.

3. **f(z) = 2 (1/2)^x**: The base is 1/2, which is less than 1. This also represents exponential decay.

4. **f(z) = 5 (1/6^x)**: This can be rewritten as f(z) = 5 * (6^(-x)), which indicates exponential decay as the base is less than 1 when expressed in this form.

Based on this analysis, the equation that represents exponential growth is:

**f(z) = 2 (3)^x**.