Activity
1. Desmos activity: Exponential Graph Maps
Link to Learning
Log into student.desmos.com using the information provided by your teacher to complete the activity.
2. Functions and are defined by these equations:
a. Use the graphing tool or technology outside the course. On the same coordinate plane, sketch a graph that represents the functions, and . It may be helpful to use a different color for each function.
Compare your answers:
b. Which function is decaying more quickly?
c. Explain your reasoning regarding which function decays more quickly.
Compare your answers:
has a smaller base than . Both bases are less than 1, so both functions decrease, but decreases more rapidly.
Building Character: Grit
Grit predicts accomplishing challenging goals of personal significance. For example, grittier students are more likely to graduate from high school, and grittier cadets are more likely to complete their training at West Point.
Think about your current sense of grit. Are the following statements true for you?
- There is at least one subject or activity that I never get bored of thinking about.
- I finish whatever I begin.
Don’t worry if none of these statements are true for you. Developing this trait takes time. Your first step starts today!
Self Check
Additional Resources
Matching Exponential Functions and Graphs
For each of the following, match each function with one of the graphs in the picture below.
Remember, the equation for an exponential function is . The will affect the -intercept. When , there is exponential decay. The closer is to 0, the faster it decays. The closer is to 1, the slower it decays. When , the larger the value of , the faster it grows.
Equation | -intercept | Growth/Decay | Match |
|
Decay | B | |
|
Growth | F | |
|
Decay | A | |
|
Growth | D | |
|
Growth | E | |
|
Decay | C |
Try it
Try It: Matching Exponential Functions and Graphs
In the graph above, which function, , has the largest value for ?
Compare your answer:
Here is how to identify which has the largest value for :
In the function , changes the -intercept. The function with the largest -intercept is C. It crosses the -axis at the highest point.