Pay

Paying it Forward
Introduction to Exponential Functions
Objective: Students will be able to identify and explain key difference
between linear functions and exponential functions.
Intro/Launch – 10 Minutes
 Show video
 Discussion
o What is the pay it forward movement?
o What was Trevor’s idea?
 Reflection 3-5 Minutes
o Write down 3 ideas you have for helping someone
o Draw a model that represents what happens if those three
people pass it on and then those people pass it on.
 Discussion
o Have a student share their model on the board
o How many people were helped initially? How about after
the first iteration?
o How many iterations do you think it would take to affect
everyone at RAILS? How about the world? What information
would we need?
Exploration
Discussion
 Desmos Graph projected and table on the board.
 Using Trevor’s model, how many iterations would it take to reach
everyone in the world?
 Using the linear model, how many iterations would it take?
 Which model is most effective? Why?
 How did you get from one stage to the next? (adding v.
multiplying)
 What does the point of intersection represent?
 What roadblocks might you run into when trying to reach out to
people?
 What would be our algebraic expression for each model?
o y=b*a^x
 a=ratio/change
 x=iteration
 b=starting point
 MULTIPLYING
o y=mx + b
 m= change/slope



 x= iteration
 b=starting point
 ADDING
Can you come up with any other scenarios that use an
exponential model?
o Ice bucket challenge
o Pyramid schemes

Summary:
 Exponential functions
straight lines
 Exponential functions
 Exponential functions
 Exponential functions
look like y=mx+b

make curves and linear functions make
grow a lost faster than linear
have a common ratio (b)
look like y=a*b^x and Linear functions

NAME: ______________________
PAY IT FORWARD
Is it possible for one idea to change the world?
1. Complete the table below to determine the number of people
affected during each stage of the process.
Stage
1
2
3
4
5
6
7
8
9
10
of
Proces
s
Numb 3
9
27
er of
People
Effecte
d
2. Is there a pattern? Describe in words how the number of people
affected changes with each stage of the process.

3. Use the graph below to graph the points that will fit. Describe the
shape.

4.

Suppose
instead
paying
forward,

of
it

everyone in your Algebra 1 class pledged to help one person
every day. Complete the table below to determine the number of
people affected.
Stage
1
of
Proces
s
Numb
er of
People
Effecte
d

2

3

4

5

6

7

5. Graph the points that will fit on the graph above.

8

9

10

6. What differences do you notice between the two graphs?

7. Which model do you think is most effective? Justify your answer.