Describe how you can tell if there is growth or decay rate in an exponential equation. (2 points)

Question

Give an example of an exponential growth or decay equation. (1 point)

Answer 1

To determine whether an exponential equation represents growth or decay, you can examine the base of the exponential function in the equation, usually of the form \( y = a \cdot b^x \), where:

1. If \( b > 1 \): The equation represents exponential growth because the values of \( y \) increase as \( x \) increases.
2. If \( 0 < b < 1 \): The equation represents exponential decay because the values of \( y \) decrease as \( x \) increases.

Example of an Exponential Growth Equation:

An example of exponential growth is \( y = 3 \cdot 2^x \).

Example of an Exponential Decay Equation:

An example of exponential decay is \( y = 5 \cdot (0.5)^x \).