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

Question

Responses

y=4(13)xy is equal to 4 times 1 third to the x th power

y=2(2.0)xy is equal to 2 times 2 point 0 to the x th power

y=3(4.7)xy is equal to 3 times 4 point 7 to the x th power

y=8(0.2)xy 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 a function increases at a rate proportional to its current value, typically characterized by a base greater than 1 when expressed as \(y = a \cdot b^x\) where \(b > 1\).

Let's analyze the given equations:

1. \(y = 4(1/3)^{x}\): This represents exponential decay since \(1/3 < 1\).

2. \(y = 2(2.0)^{x}\): This represents exponential growth because \(2.0 > 1\).

3. \(y = 3(4.7)^{x}\): This also represents exponential growth since \(4.7 > 1\).

4. \(y = 8(0.2)^{x}\): This represents exponential decay because \(0.2 < 1\).

5. \(y = 6(1 - 0.75)^{x} = 6(0.25)^{x}\): This represents exponential decay since \(0.25 < 1\).

In summary, the equations that represent exponential growth are:

• \(y = 2(2.0)^{x}\)
• \(y = 3(4.7)^{x}\)