Question

Select the following equations that represent exponential growth.

Answer Options:

y=4(
2
1
​
)
x

y=2(2.0)
x

y=3(4.7)
x

y=8(0.2)
x

y=6(1−0.75)
x

Answer 1

To identify the equations that represent exponential growth, we look for equations of the general form \( y = a \cdot b^x \) where:

- \( a \) is a positive constant (initial value)
- \( b \) is a positive constant greater than 1 (growth factor)

Let's evaluate each of the given equations:

1. **\( y = 4(2^x) \)**: This equation represents exponential growth because \( b = 2 \) (which is greater than 1).

2. **\( y = 2(2.0^x) \)**: This represents exponential growth as \( b = 2.0 \) (which is also greater than 1).

3. **\( y = 3(4.7^x) \)**: This is an exponential growth equation as well since \( b = 4.7 \) is greater than 1.

4. **\( y = 8(0.2^x) \)**: This does not represent exponential growth because \( b = 0.2 \) is less than 1, which would indicate exponential decay.

5. **\( y = 6(1 - 0.75)^x \)**: This simplifies to \( y = 6(0.25)^x \), which also does not represent exponential growth because \( b = 0.25 \) is less than 1, indicating exponential decay.

Therefore, the equations that represent exponential growth are:

- \( y = 4(2^x) \)
- \( y = 2(2.0^x) \)
- \( y = 3(4.7^x) \)