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). 
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