Describe the transformations that would be
made to y = 3x.
1. y  2(3)
x 5
1
Stretch 2, Right 5, Up 1
Growth Model
Reflect across x-axis,
1 x
2. y   (3)  4 Shrink 1/3, down 4
Neither
3
Is this a growth or decay model or neither?
The swans on Elsworth Pond have been
increasing in number each year. Felix has been
keeping track and so far he has counted 2, 4, 7,
17, and 33 swans each year for the past five
years.
1) Make a scatter plot of the data.
2) Is this a linear or exponential
model? Exponential
3) How many swans should Felix
expect next year? 64
Review Homework
Skills Check
Transformations
CC Coordinate Algebra
UNIT QUESTION: How can we use
real-world situations to construct and
compare linear and exponential
models and solve problems?
Standard: MCC9-12.A.REI.10, 11, F.IF.1-7, 9, F.BF.1-3, F.LE.1-3, 5
Today’s Question:
How is interest earned in the bank
modeled with an exponential
equation?
Standard: MMCC9-12.F.LE.1
y  P 1  r  y  P 1  r 
t
y = balance
y = balance
P = initial
P = initial
t = time in years
t = time in years
r = % of increase
r = % of decrease
1+r = growth factor
1-r = decay factor
t
In 2000, the cost of tuition at a state
university was $4300. During the next
8 years, the tuition rose 4% each year.
• Write a model the gives the tuition y (in
dollars) t years after 2000. y = 4300(1
• What is the growth factor?
+ .04)t
1.04
• How much would it cost to attend college in
2010? In 2015? f(2010) = 6365.05
f(2015) = 7744.06
• How long it will take for tuition to reach
$9000? 19 years, 2019, $9059.45
A 2010 Honda Accord depreciates at
a rate of 11% per year. The car was
bought for $25,000.
• Write a model the gives the value of the
car y (in dollars) t years after 2010.
y = 25,000(1 – .11)t
• What is the decay factor?
.89
• How much is the car worth now? In 2015?
f(2014) = 15,685.56
f(2015) = 13,960.15
• How long will it take for my car to be worth
half?
6 years, 2016, $12,424
Extension
• What “r” value would be used if the
principal is being doubled every
year?
2
• What about if it is tripled every
year?
3
Suppose you start work at $600 a
week. After a year, you are given
two choices for getting a raise:
•Opt. 1: 2% per weeky = 6000(1 + .02)t
•Opt. 2: a flat $15 a week raise for each
successive year.
y = 15x + 600
Which option is better after a year?
Option 1 gets you more money
Which option has the greatest ROC from [3, 6]?
Option A
Option B
An investment of $1,000
earns interest at a rate of
3.75%, compounded
monthly.
y=
1000(1.0375)t
1247.18  1116.77
m
63
m  43.47
1200  1100
m
63
m  33.3
Option A has a greater ROC from [3, 6].
Classwork
Practice Worksheet
5 problems
y  P 1  r 
t
y  P 1  r 
t
Homework
Worksheet 9 problems
y  P 1  r 
t
y  P 1  r 
t