Chapter 3, Problem 118RE

To determine

Describe characteristics of graph for the positive and negative value of k.

Answer to Problem 118RE

The graph of $y=e^t$ is monotonically increasing while the graph of $y=e^{-t}$ is monotonically decreasing

Explanation of Solution

Given:

Equation of graph:

  $y=e^{kt}$

Let’s describe the characteristics of the graph of $y=e^{kt}$ , when $k$ is positive and when $k$ is negative.

Let assume $k$ is 1 when it is positive and −1when it is negative.

Let us draw the graph of the function $y=e^t$

  

Let us draw the graph of the function $y=e^{-t}$

  

It is observed by comparing the two different graphs that the graph of $y=e^t$ is monotonically increasing while the graph of $y=e^{-t}$ is monotonically decreasing.