Question

Select the following equations that represent exponential growth. (1 point)
Responses

y=4(1/3)x

y is equal to 4 times 1 third to the x th power
y=2(2.0)x
y is equal to 2 times 2 point 0 to the x th power
y=3(4.7)x
y is equal to 3 times 4 point 7 to the x th power
y=8(0.2)x
y is equal to 8 times 0 point 2 to the x th power
y=6(1−0.75)^x

Answer 1

Exponential growth occurs when the base of the exponential function is greater than 1. Let's evaluate each of the provided equations:

1. **y = 4(1/3)^x**: The base is \( \frac{1}{3} \), which is less than 1. This represents exponential decay.

2. **y = 2(2.0)^x**: The base is \( 2.0 \), which is greater than 1. This represents exponential growth.

3. **y = 3(4.7)^x**: The base is \( 4.7 \), which is greater than 1. This represents exponential growth.

4. **y = 8(0.2)^x**: The base is \( 0.2 \), which is less than 1. This represents exponential decay.

5. **y = 6(1−0.75)^x**: This simplifies to \( y = 6(0.25)^x \) since \( 1 - 0.75 = 0.25 \). The base \( 0.25 \) is less than 1, which represents exponential decay.

Based on this evaluation, the equations that represent exponential growth are:

- **y = 2(2.0)^x**
- **y = 3(4.7)^x**