+
CCM1 Unit 5
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Warm Up – January 23
Complete the student Information
sheet on your desk.
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What Do I Remember
Spend
15 minutes going though the
“What Do I Remember” worksheet
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What you should have
remembered 
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Mean-
average
Median-
middle number
Describing
Data- SOCS
Standard
Deviation- How much
variation exists from the average
Range-The
difference between
the highest and lowest number
+  Box Plot- Use the 5 number summary

Dot Plot-

Histogram-
+ 5 Number Summary- Minimum,
Q1, Median, Q3, and Maximum
IQR- The difference between
Q3 and Q1

Outliers-
A number that is
numerically distant from the rest
of the data
+  Categorical – data that can be separated by
category
EX) sorting students by the model of car
they have
 Quantitative
– data that can be separated by
numerical values
EX) sorting students by the number of
siblings they have
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Algebraic
Expressions- Does not have
an equal sign, You evaluate Algebraic
Expressions
Algebraic
Order
Equations- has an equal sign
of Operations- (PEMDAS)
 Parenthesis
 Exponents
 Multiplication/Division
 Addition/Subtraction
Evaluate-
means to solve
+ Solving Equations- Follow reverse order
of operations to get the variable by its
self on one side of the equation
Whole
Numbers- Includes zero and all
the positives (no fractions or decimals)
Integer-
Includes all negatives, zero, and
all positives (No fractions or decimals)
Variable-
a symbol that stands for a
number
 Ex)
x – 2 = 10
X is the variable
+ Subtracting Negatives- Keep,
change, change
Multiplying Negatives Neg *Neg = Pos
 Neg*Pos = Neg
 Pos * Neg = Neg
 Pos*Pos = Pos
Dividing Negatives
 Neg /Neg = Pos
 Neg/Pos = Neg
 Pos /Neg = Neg
 Pos/Pos = Pos
Property- Distribute to EVERYTHING inside the
+ Distributive
parenthesis

Constant- just a number, does not have a variable

Coefficient- The NUMBER in front of (multiplied by) a variable

Like Terms-Terms with the same exact variables

Substitution- Putting a number in place of a variable to simplify an
expression

Equivalent expression- two expressions that have the same most
simplified form

Solving Equation- Follow reverse order of operations to get the
variable by its self on one side of the equation
+ Less Than <

≤

Less than or equal to

Greater Than

Greater Than or Equal To

Open Circle- Use for

>
≥
< or >
Closed Circle- Use for ≤or ≥
 Solving
Inequalities- Solve like you solve
equations; Follow reverse order of operations
+ Domain
 Independent Variable
 X’s
 Goes
on x-axis
 Goes in L1 when finding line of best fit
Range
 Dependent Variable
 Y’s
 Goes
on y-axis
 Goes in L2 when finding line of best fit
+ Function Notation
f(x)
=
Example: f(x)= 2x + 4
Now-Next
Rule: A recursive rule
found by relating a number to
what comes before it.
Written
as
Ex) NEXT = NOW + 4
 NEXT = NOW/2

+  Direct Variation


Equation: y=kx
K = constant of variation
Goes through the origin on a graph
 Finding slope
 (x1, y1)
 (x2, y2)
through 2 ordered pairs:
 Slope- Intercept Form:
 M = slope; B = y-intercept
y = mx + b
 Point Slope: y – y1 = m( x – x1)
 M = slope; X1, y1 are from the ordered pair
 Standard Form: Ax + By =
 No Fractions, C is a constant
C
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Parallel
Lines- never intersect,
have the SAME SLOPE
Perpendicular
Lines- Slopes are
opposite reciprocal
+
change to –
 – change to +
Flip the fraction
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Pay It Forward

http://www.youtube.com/watch?v=DvKAP
HvCPS8


To 1:17
http://www.youtube.com/watch?v=vmboo
6cj8ds

From 3:10 to 4:39
1. How many people would
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receive a Pay It Forward good
deed at each of the next
several stages of the process?
Stage 1:
Stage 2:
Stage 3:
Stage 4:
Stage 5:
Stage 6:
2. What is your best guess for the number of people
who would receive Pay It Forward good deeds at
the tenth stage of the process?
+3. Which of the graphs below do you think is
most likely to represent the pattern by which
the number of people receiving Pay It
Forward good deeds increases as the
process continues over time?
Graph Number:
___________
+4. Take your values for each stage (from #1)
and graph the data. Hint: Your x-axis needs
to be the stage number and your y-axis
needs to be the number of people receiving
Pay It Forward.
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Mathematical terminology
This graphs represents EXPONENTIAL
growth.
These data sets display properties of
EXPONENTIAL FUNCTIONS.
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+
Warm Up – January 24th
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Exponent Rules Review
Exponents are a “short-hand” way
of multiplying the same quantity
over and over.
Example:
X4 = (x)(x)(x)(x)
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Try Some: Expand the following
43
Y4
X2y5
w6z1
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Using Exponents to simplify
Write using exponents
X*x*x*x
2*2*2*2*x*x*x*y*y
3*3*3*4*4*4*4*x
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Zero as an exponent
Anything
equals 1.
Ex
x0 = 1
 60
=
Y0
=
with an exponent of zero
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Negative Exponents
When
you have a NEGATIVE exponent
you turn it POSITIVE and FLIP it.
EX
x-3
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Try Some
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Multiplication
When
multiplying like bases you ADD
exponents
Ex: x4x2
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Try some!
X3x4
Y3x4y7
z3y2x5z5y6x10
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Exponents of Exponents
 When
you have an exponent of an exponent
you MULTIPLY
 EX: (x4)3
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Try Some!
(x)5
(x2y4)5
(2x3)6
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Division
When
you divide like bases you
SUBTRACT exponents
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Try Some
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Growing Sequences
 Arithmetic
Sequence : goes from one term to the
next by always adding (or subtracting) the same
value
 Common
Difference : The number added (or
subtracted) at each stage of an arithmetic sequence
 Initial Term
: Starting term
For example, find the common difference and the next
term of the following sequence:
3, 11, 19, 27, 35, . . .
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Growing Sequences
 Geometric
Sequence: goes from one term to the
next by always multiplying (or dividing) by the
same value
 Common
Ratio: The number multiplied (or
divided) at each stage of a geometric sequence
Determine the common ratio r of the Brown Tree
Snake Sequence.
1, 5, 25, 125, 625, . . .
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+
Warm Up – January 25th
+The geometric sequence from the Brown
Tree Snake problem (1, 5, 25, 125, 625 . .
.) can be written in the form of a table, as
shown below:
The Brown Tree Snake was first
introduced to Guam in year 0. At the
end of year 1, five snakes were found; at
the end of year 2, twenty-five snakes
were discovered, and so on…
+ Since we now have a table of the
information, a graph can be drawn, where
the year is the independent variable (x)
and the number of snakes is the dependent
variable (y). See below:
+
The curved graph of this problem situation is
known as an exponential growth function. An
exponential growth function occurs when the
common ratio r is greater than one.
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Group Work
In
your group’s complete the
worksheet handed out.
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Tuesday, January 29th
Warm Up # 4
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Homework Check – 5.4
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What is the difference between an arithmetic and geometric
sequence?
What is the difference between a common ratio & a common
difference? Which type of sequence does each go with?
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The Ladybug Invasion
As a biology project, Tamara is studying the growth of a
ladybug population. She starts her experiment with 5
ladybugs. The next month she counts 15 ladybugs.
1) The ladybug population is growing arithmetically. How
many beetles can Tamara expect to find after 2, 3, and 4
months? Write the sequence.
2) What is the common difference?
3) Now put the sequence into a table in the space below.
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4) How long will it take the ladybug
population to reach 200 if it is
growing linearly?
+5) Suppose the ladybug population is
growing exponentially. How many
beetles can Tamara expect to find
after 2, 3, and 4 months? Write the
sequence.
6) What is the common ratio?
7) Now put the sequence into a table in
the space below.
+8) How long will it take the ladybug
population to reach 200 if it is growing
exponentially?
9) Why does it take the ladybug population
longer to reach 200 when it grows linearly?
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10) Graph both tables on the designated graphs provided
below. Be sure to label your axes
Linear Growth
Exponential Growth
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Homework
Worksheet 5.5
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Wednesday January 30
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Warm Up - # 5
Homework 5.5
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One Grain of Rice
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Exponential Functions
An exponential function is a function with
the general form
y = abx
a ≠ 0 and b > 0, and b ≠ 1
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A and B
A is your starting value
B is growth factor
X is time
Y is the amount after time
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Starting Value and Growth Factor
Identify each starting value and the growth
factor.
1.
Y= 3(1/4)x
2.
Y= .5(3)x
3.
Y = (.85)x
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Modeling Exponential Functions
Suppose 20 rabbits are taken to an island. The
rabbit population then triples every year.
The function f(x) = 20 • 3x where x is the
number of years, models this situation.
What does “a” represent in this problems? “b”?
How many rabbits would there be after 2 years?
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Modeling Exponential Functions
Suppose a Zombie virus has infected 20 people
at our school. The number of zombies doubles
every day. Write an equation that models this.
How many zombies are there after 5 days?
If there are 1800 students at Knightdale, how
long will it take for the Zombie virus to infect
the whole school?
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3. A Bacteria culture doubles in size every
hour. The culture starts at 150 cells.
How many will there be after 24 hours?
After 72 hours?
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4. A population of 2500 triples in size
every year.
What will the population be in 30 years?
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+
Warm up
Homework
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Remember Exponential Functions
An exponential function is a function with the
general form
y = abx
a ≠ 0 and b > 0, and b ≠ 1
A is your starting value
B is growth factor
X is time
Y is the amount after time
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Intervals of Time
In an exponential equation when
your growth factor happens over a
special interval of time, we must
divide our x by that interval.
y = ab
x
n
n is your interval of time
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Modeling Exponential Functions
Suppose a Zombie virus has infected 20
people at our school. The number of
zombies doubles every 30 minutes. Write
an equation that models this.
How many zombies are there after 5
hours?
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4. A
population of 2500 triples in size
every 10 years.
What
will the population be in 30
years?
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Friday February 1st
Compound Interest
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Warm Up
Homework
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Review
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Quiz
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Compound Interest
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Decimals as Percent's
To Write a Decimal as a Percent:
Move decimal place 2 places right.
Ex:
.3434
.25
1.736
2.2798
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Percent's as Decimals
To Write a Percent as a Decimal:
Move decimal place 2 places left.
Ex:
45%
63.3%
100.5%
5.64%
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Compound Interest
Compound Interest is another type exponential function:
nt
Here
æ rö
A = P ç1+ ÷
è nø
P = starting amount
R = rate (AS A DECIMAL!!!!)
n = period
T = time
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Compound Interest
Find the balance of a checking
account that has $3,000 compounded
annually at 14% for 4 years.
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Compound Interest
Find the balance of a checking
account that has $500 compounded
semiannually at 8% for 5 years.
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Transformations
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Warm Up
Homework
Compound Interest Practice
Go over Review Sheet
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Transformations
Remember: Translations are
moments of a function!
Complete Worksheet
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Transformation Sum Up
y = 2x-h + k
+ h left
- h right
-k
down
+ k up
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Part of an Exponential Graph
Horizontal Asymptote: A horizontal line
that the graph “flat lines” at
Y-Intercept: Where the graph crosses
the y-axis.
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Identify Horizontal Asymptotes
and y-intercept
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Identify Horizontal Asymptotes
and y-intercept
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Write an Equation if the Base = 2
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Write an Equation if the Base = 2
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Write an Equation if the Base = 2
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Exponential Decay
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Warm UP
Homework
Finish Translations
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Drug Filtering
Assume that your kidneys can filter out 25% of a drug in your blood every
4 hours. You take one 1000-milligram dose of the drug. Fill in the table
showing the amount of the drug in your blood as a function of time. The
first three data points are already completed. Round each value to the
nearest milligram
Time since taking the drug (hrs)
Amount of drug in your blood (mg)
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
1000
750
562
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+
+
3.
How many milligrams of the drug are in your blood after 2 days?
4.
Will you ever completely remove the drug from your system?
Explain your reasoning.
5.
A blood test is able to detect the presence of the drug if there is
at least 0.1 mg in your blood. How many days will it take before
the test will come back negative? Explain your answer.
+
Recall: y = a•bx
Initial (starting) value = a
Growth or Decay Factor = b
x is the variable, so we change that value based on what we are
looking for!
Remember that the growth or decay factor is related to how the
quantities are changing.
Growth: Doubling = 2, Tripling = 3.
Decay: Losing half =
Losing a third =
+
Exponential Decay
When b is between 0 and 1!
Growth : b is greater than 1
+
If the rate of increase or decrease is a
percent:
we use a base of
1 + r for growth
or
1 – r for decay
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Ex 1.
Suppose the depreciation of a car is 15% each year?
A)
Write a function to model the cost of a $25,000 car x
years from now.
B)
How much is the car worth in 5 years?
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Ex 2:
Your parents increase your allowance by 20% each year.
Suppose your current allowance is $40.
A)
Write a function to model the cost of your allowance x
years from now.
B)
How much is your allowance the worth in 3 years?
+
Complete the 2 practice problems
Other
Drug
Filtering
Problems
+
1. Assume that your kidneys can filter out 10% of a drug in your blood
every 6 hours. You take one 200-milligram dose of the drug. Fill in the
table showing the amount of the drug in your blood as a function of
time. The first two data points are already completed. Round each
value to the nearest milligram.
+ TIME SINCE TAKING
THE DRUG (HR)
0
6
12
18
24
30
36
42
48
54
60
AMOUNT OF DRUG
IN YOUR BLOOD (MG)
200
180
+
+
A)
How many milligrams of the drug are in your blood after 2
days?
B)
A blood test is able to detect the presence of the drug if
there is at least 0.1 mg in your blood. How many days will
it take before the test will come back negative? Explain
your answer.
+
2. Calculate the amount of drug remaining in the blood in the
original lesson, but instead of taking just one dose of the
drug, now take a new dose of 1000 mg every four hours.
Assume the kidneys can still filter out 25% of the drug in
your blood every four hours. Have students make a complete
a table and graph of this situation.
+
TIME SINCE TAKING
THE DRUG (HR)
0
4
8
12
16
20
24
28
32
36
40
44
48
AMOUNT OF DRUG
IN YOUR BLOOD (MG)
1000
1750
2312
+
+
A)
How do the results differ from the situation explored during the
main lesson? Refer to the data table and graph to justify your
response.
B)
How many milligrams of the drug are in your blood after 2 days?
+
HW 5.10
+
Growth VS Decay
and Percent Growth and Decay
+
Exponential Functions Remember!
An exponential function is a function
with the general form
y = abx/n
a ≠ 0 and b > 0, and b ≠ 1
+
A and B
A Starting Value
B is direction
Growth
Decay
b>1
0<b<1
+
Y-Intercept and Growth vs. Decay
Identify each y-intercept and whether it is a
growth or decay.
1.
Y= 3(1/4)x
4.
Y = 300(1.3)x
2.
Y= .5(3)x
5.
Y = 4500(.4)x
3.
Y = (.85)x
6.
Y = 76(3/4)x
+
Increase and Decrease by percent
Exponential
Models can also be used
to show an increase or decrease by a
percentage.
+
Increase and Decrease by percent
The rate of increase or decrease is a
percent, we use a change factor/base
of 1 + r or 1 – r.
Growth
Decay
b>1
0<b<1
Change factor
Change Factor
(1 + r)
(1 - r)
.
+
Percent to Change Factor
When something grows or decays by a
percent, we have to add or subtract it
from one to find b.
1.
Increase of 25% 2. increase of 130%
2.
Decrease of 30% 4. Decrease of 80%
+
Growth Factor to Percent
Find the percent increase or decease from
the following exponential equations.
1.
Y = 3(.5)x
2.
Y = 2(2.3)x
3.
Y = 0.5(1.25)x
+
Percent Increase and Decrease
A dish has 212 bacteria in it. The population
of bacteria will grow by 80% every day.
How many bacteria will be present in 4
days?
+
Percent Increase and Decrease
 The
house down the street has termites in
the porch. The exterminator estimated that
there are about 800,000 termites eating at
the porch. He said that the treatment he put
on the wood would kill 40% of the termites
every day.
 How
many termites will be eating at the
porch in 3 days?