Download Algebra 1, Unit 4 - Southwest Washington Mathematics

EX.0 Introduction to Exponential Functions
TEACHER: Saving Money
Exponential Functions Learning Targets
Practice 1. Make sense of problems and persevere in solving them.
Practice 2 Reason abstractly and quantitatively.
F.BF.1 Write a function that describes a relationship between two quantities. 
1a. – Determine an explicit expression, a recursive process, or steps for calculation from a
context.
F-BF I can build a function.
 Write an explicit equation for an exponential situation described in words, graphs or in tables.
F-LE.1
F-LE I can construct and compare linear, quadratic and exponential models and solve
problems.
 Show that linear functions result from repeated addition and exponential functions result from
repeated multiplication.
Purpose: This is a unit launch task. It compares a linear and an
exponential growth.
In this task, we want students to see that an exponential function grows
much faster than a linear function. We expect students to find the
quantities with recursive reasoning only.
Language:
rate of change
percent increase
percent decrease
growth factor
We don’t expect students to use the exponential function f (x)  a 1.02  , but expect
x
f (x)  a  a 0.02 if they can write any equation at all.
x
Students will learn to multiply by the growth factor, in this case 1.02, in a later unit.
What to bring out in the Debrief:
The cookie jar savings is a linear function, which has a constant rate of change.
The savings account is an exponential function, which grows by multiplying the
growth factor, 0.02, times the previous amount and adding that product to the
previous amount.
Assessment:
Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative
Commons Attribution 4.0 International License. 2014-2015
Page 1 of 3
EX.0 Introduction to Exponential Functions
TEACHER: Saving Money
Big Idea A: Students will create multiple representations of exponential
relationships and move flexibly between them (graphs, tables, pictures, situations,
equations).
 F-BF.1 – Write a function that describes a relationship between two quantities.
1.a – Determine an explicit expression, a recursive process, or steps for calculation
from a context.
Big Idea D: Students will compare and interpret similarities and differences of
multiple representations of exponential relationships (graphs, tables, pictures,
situations, equations). Students will also compare exponential to linear functions.
 F-LE.1 Distinguish between situations that can be modeled with linear functions
and with exponential functions.
1a. Prove that linear functions grow by equal differences over equal intervals;
and that exponential functions grow by equal factors over equal intervals.
1b. Recognize situations in which one quantity changes at a constant rate per unit
interval relative to another.
1.c – Recognize situations in which a quantity grows or decays by a constant
percent rate per unit interval relative to another.
Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative
Commons Attribution 4.0 International License. 2014-2015
Page 2 of 3
EX.0 Introduction to Exponential Functions
TEACHER: Saving Money
Jacob’s grandparents started saving for his college fund. They put $5,000 in a cookie jar when he
was born. They added $50 every year on his birthday to the cookie jar.
Jacob’s parents started saving for his college fund. They put $4,500 in a savings certificate at a
bank that earned 2% annual interest when he was born. They did not add any money to the
certificate.
1. Before you do any calculations, guess whether
Jacob will have more money in the cookie jar or in
the bank by his 18th birthday.
2. Explain the reasoning you used to that choice.
3. Complete the table to show how much is in
Jacob’s grandparents’ cookie on his 18th birthday.
4. Find a function that Jacob can use to determine
the amount in his cookie jar as a function of his
age.
g(x) = ______ 5000  50x ___________________
5. Make a table to show how much is in Jacob’s
college fund on his 18th birthday.
6. Find a function that Jacob can use to determine
the amount in his cookie jar as a function of his
age.
 
x
p(x) = __ 4500  4500 0.02 ______
7. By his 18th birthday, did Jacob have more money
in the cookie jar or in the bank?
savings account
8. Which savings grew faster, the cookie jar or the
bank account?
Grandparents’
Savings
Year Money $
x
g(x)
0
5000
Parents’
Savings
Year Money $
x
p(x)
4500
0
1
5050
1
4590
2
5100
2
4682
3
5150
3
4775
4
5200
4
4871
5
5250
5
4968
6
5300
6
5068
7
5350
7
5169
8
5400
8
5272
9
5450
9
5378
10
5500
10
5485
11
5550
11
5595
12
5600
12
5707
13
5650
13
5821
14
5700
14
5938
15
5750
15
6056
16
5800
16
6178
17
5850
17
6301
18
5900
18
6427
The savings account
9. Explain the reasoning you used to that choice.
The money in the cookie jar grows at a constant rate of $50 each year. The savings
account grew $90 the first year, and by the last year grew $126.
Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative
Commons Attribution 4.0 International License. 2014-2015
Page 3 of 3