Decide whether each situation is best described by a linear, quadratic, or exponential function.
If the function is exponential: What is the growth factor. Is it doubling (factor of 2)? Tripling (factor of 3)? Factor of 5? 10?

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 coefficients 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 posted their animation of a puppy doing a back flip into a pile of laundry and the meme went viral! Every person that sees the meme falls in love with it and shares it with 10 new friends.

6 Is the function increasing or decreasing?

7 When the student posts it (x=0), how many total times has it been shared?

8 How many times will it have been shared after…​

(the next person shares)
x=1
(their friends share)
x=2
x=3 x =4

9 What is the form of this function? linear ☐ quadratic ☐ exponential

10 If it’s exponential,

Fill in the coefficients to write a function that shows how many times the meme has been shared after a given number of "share cycles":

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). CCbadge 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.