Decide whether each situation is best described by a linear, quadratic, or exponential function.
If the function is exponential: Identify the growth factor and the initial value.
High Fives
Two students started a club. At every meeting, students in attendance must high-five each of the other students. Club membership has been growing steadily by one student each meeting.
1 Is the function increasing or decreasing?
2 When the 2 students started the club (x=0), how many high-fives happened?
3 How many high-fives happen at the subsequent meetings…
| (3 students) x=1 |
(4 students) x=2 |
x=3 | x=4 |
|---|---|---|---|
|
4 What is the form of this function? linear ☐ quadratic☐ exponential☐
5 If it’s exponential,
Fill in the blanks to write a function that shows the how many high-fives happen for a given number of students:
f(x) = initial value a × growth factor b x + horizontal asymptote k
Is it exponential growth? ☐ or decay? ☐
Going Viral
A student shared a video of a dog doing a back flip into a pile of laundry. No one else shared it that day, but the next day it went viral, and the number of shares increased 10x every day!
6 Is the function increasing or decreasing?
7 How many total shares did the video have on the first day (x=0), when the student posted it?
★ How many total shares happened each day after that…
| (the next day) x=1 |
(the day after that) x=2 |
x=3 | x=4 |
|---|---|---|---|
|
8 What is the form of this function? linear ☐ quadratic ☐ exponential☐
9 If it’s exponential,
Fill in the blanks to write a function that shows how many times the meme has been shared in total after a given number of days:
f(x) = initial value a × growth factor b x + horizontal asymptote k
Is it exponential growth?☐ or decay? ☐
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.