Exponential Functions
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Define:
◦ Arithmetic Sequence: A pattern that… repeats
addition over and over.
◦ Geometric Sequence: A pattern that… repeats
multiplication over and over.
◦ Notes: Recognizing each sequence:
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Notes: d vs. r
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Define:
◦ Appreciation
◦ Depreciation
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Story Problem #1: pg. 40 Example A
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Story Problem #2: pg. 42 Example B
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Warm up:
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Pg. 259 Investigation:
◦ Work on steps 1-10 as a group. You will be called
upon as a table group for solutions.
◦ (see next page for investigation)
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Notes: Recap of all Rules pg. 260
(rewrite them again from this page)
Challenge Problem: Simplify pg. 265 (Mr.
Higgins wife breakfast request)
𝐸𝑎𝑠 −1 𝑡𝑒𝑟 0 (𝐸𝑔𝑔)
𝑦
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Warm up: Simplify with no negative
exponents
Notes: Solving with exponents:
◦ Method #1: Exponential functions-similar
bases(read example A pg. 260)
 step 1: find similar bases, rewrite exponents
 step 2: set the exponents equal to each other
◦ Method #2:Power Functions-Undo the exponent
(read example B pg.262)
 step 1: balance the equation until there is a single
term and single exponent
 step 2: undo the exponent by a radical or fractional
exponent
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Warm up: similar bases
Review: Solving functions
◦ Similar Bases (create our own)
◦ Undo the Exponent (work on unfinished prob’s)
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New Lesson: simplify radicals pg. 250
◦ Example A: Estimating value of a square root
◦ Example B: Simplifying Square roots
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Warm up: Define (look up in glossary if need)
◦ Asymptote
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Investigation of Exponential Graphs (not in book).
When sketching each graph, plot at least 3 points
(just like square root functions, etc). 10 minutes
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Graph y = 2𝑥 . Write the domain, range, asymptote.
Graph y = 2𝑥 +3. Write the domain, range, asymptote.
Graph y = 4 ∗ 2𝑥 . Write the domain, range, asymptote.
Graph y = 2𝑥−1 . Write the domain, range, asymptote.
Graph y = 2𝑥/3 . Write the domain, range, asymptote.
Answer the questions:
 What was the parent function?
 What part of the graph did the transformations affect?
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General Exponential Equation Definition
◦ y = 𝑏 𝑥 , where b is the base of the exponent. In a
real world setting b=growth rate.
◦ y = 𝑎 ∗ 𝑏 𝑥 , where b is the growth rate, and a is the
initial value/y-intercept
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Worksheet: exponential Transformations WS
in class
Homework is from the book.
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Notes: Rational Exponents pg.267
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Practice:
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Notes: General Equation of Exponential
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Notes: Point Ratio Form
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Practice:
◦ You invest $2000 in a savings account. It pays 3.5%
annual interest. Write the exponential equation of
money in terms of years. Find the amount in the
account after 5 years.
◦ You purchase a car for $24,000. It loses 10% of its
value each year. Find the value of the vehicle in 20
years.
◦ Bacteria doubles every hour. You check the petri
dish and find 50 bacteria present in the culture at 4
hours. Write an equation in point-ratio form. Find
the amount of bacteria at 12 hours.
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Lesson: How to solve for the growth rate.
◦ Ex. Given 2 points of and exponential function *This method is
NOT in book
◦ Set up:
 Write in y = 𝑎 ∗ 𝑏 𝑥 , substitute x and y
 Use division to eliminate a
 Use exponent rules to isolate b
◦ Practice: (2, 18) and (6, 91.125), find the growth rate, b.
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Group Activity:
◦ You will be paired in groups of 3 or 4 via random selection
◦ Each group member must write the solutions to the problems on
their “map”. They will be collected at the end of the period.
◦ When you get to each problem, write down the given information,
and work the problem out (take a calculator w/ you)
◦ Check your solutions at the front table.
◦ Your team goal is to finish all 6 problems TOGETHER. Do not
split up work among members. Finish what is reasonable for
your group. Individual scores are based on how many problems
the majority of the class finishes and the amount of work shown
for each problem.
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Warm up:
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Recap:
◦ General Equation for Exponential Equation
◦ Point-Ratio Equation for Exponential Equation
◦ How to solve for the growth rate from 2 points
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Group Activity
◦ Each group is assigned 1 lesson
◦ Using WHITE PRINTER PAPER ONLY, write the
following:
 Title of Lesson
 3 main topics of lesson
 2 sample problems that cover all 3 topics (using a, b,
etc is ok).
◦ Present for 2 minutes. Each person in group must
speak
◦ Work out the 2 problems given to you. Show all
work.
◦ Homework: Review packet, do at least 2 pages
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Warm up: given the function, what is the
domain, range, and asymptote? y  5(.4)  7
Notes: pg. 282(notation too)
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Example B pg. 282
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x 3
◦ Find the inverse of the function
◦ Graph f(x) and (f-1(x)). What do you notice?
◦ Find the composition of f(f-1(x))
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Reminder: quiz 5.1-5.4 tomorrow! (Does not
include this lesson)
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Warm up: Solve for x review
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Notes
◦ Definition of a logarithm
◦ Change of base formula of a logarithm
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1st assignment: Scavenger Hunt/Around the World activity. Turn in front of room
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Choose what CATEGORY the grade will go in.
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2nd
Assessment: score is “as is”. Check your current assessment %. IF this % is greater than current
percentage, then you will want to turn it into that category
Assignments: will be scored on completion like normal
assignment: 5.1-5.4 quiz corrections. Turn in to the back of room.
On a SEPARATE piece of paper (that will be turned in). Write up all corrections for the
assignment in this form:
#8a: Correct answer 4.5%
Why?
2 points are (0, 2741.69 ) and (5, 3416.53)
2741.69=ab5
3416.53=ab0
1.24614=b5
1.045=b
Interest rate 4.5% increase or appreciation
#3b: Correct Answer: 48x7
Why?
(-8x2)(-6x5)
Rule: multiply the coefficients-8*-6=48
x2*x*5=x7 by product property
(I accidentally multiplied the exponents
instead of adding)
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Due at the end of the period. 10 points
Grade depends on the percent of corrections you make to your quiz. More
mistakes=more corrections
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Homework : Factoring Practice. You will have time in class tomorrow to work on this
worksheet as well.
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Most important first step! GCF
2 methods for factoring:
◦ When a is one
◦ When a is not one
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Worksheet due at end of period
Extra Credit: Thanksgiving Trivia Party!
Due Monday, no exceptions, work must be
shown.
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Warm up:
Recap: Definition of a Logarithm, pg. 289 and
Change of Base Property, pg. 289, Exponential
Equations pg. 261.
Notes: Graphing Logarithms
◦ Investigation pg. 287: Exponents and Logarithms
𝑦 = 𝑙𝑜𝑔2 𝑥
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Investigation, continued
𝑦 = 2𝑥
Debrief: How are a logarithm and an exponential
graph related?
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Factor and Expand Mini Quiz
◦ Go to home and open my documents, find your
period folder and open
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Recap of the Properties
Last 2 log techniques:
◦ Using foil with logs
◦ Balancing equation with all logs on one side #23 on
back side of WS