Chapter 4.2, Problem 2E

Solution

To explain how to tell whether the function $y=b^x$ is exponential growth or decay.

Given information:

The function $y=b^x$.

Concept used:

An exponential growth model is

A decay model is given by $y=a{b}^x$ for $0<b<1$ , where $a$ is the initial amount, $b$ is the decay factor. The decay rate $r$ is related to the decay factor by the equation $b=1+r$.

Explanation:

In an exponential model of the form $y=a{b}^x$ , the term $a$ is the initial amount, $b$ is called the growth or decay factor depending on its value.

If $b>1$ , the model is called exponential growth model, and if $0<b<1$ , the model is called exponential decay model.

Therefore, in order to identify an exponential model of the form $y=a{b}^x$ as a growth or a decay, observe the value of the growth factor. If it is greater than 1, the model is growth model and if it is lies between 0 and 1, the model is a decay model