Question

Tell whether the function represents exponential growth or exponential decay. Then graph the function

18. y = 3e2x
20. y = 0.25e-3x​

Answer 1

18. y = 3e²ˣ is exponential growth.

20. y = 0.25e⁻³ˣ​ is exponential decay.

Function 18: y = 3e²ˣ

This function represents **exponential growth** because the base of the exponent,
`\( e^2 \)`, is greater than 1. In exponential growth, the quantity increases rapidly as the input variable x increases.

Graph for y = 3e²ˣ

The graph will be an upward-sloping curve that rises more steeply as x increases. The initial value
`(when \( x = 0 \)) is \( y = 3 \)`, and the curve rises exponentially from there.

Function 20: y = 0.25e⁻³ˣ

This function represents **exponential decay** because the base of the exponent,
`\( e^(-3x) \)`, is between 0 and 1. In exponential decay, the quantity decreases rapidly as the input variable x increases.

Graph for y = 0.25e⁻³ˣ

The graph will be a decreasing curve that approaches zero as x increases. The initial value when x = 0 is y = 0.25, and the curve decreases exponentially from there.

In summary, Function 18 exhibits exponential growth, and its graph rises rapidly. Function 20 represents exponential decay, and its graph decreases rapidly.