Unit 5
Reasoning about Exponential Graphs (part 1 & 2)
Intro to Exponential Functions
Lesson 12/13
HSF-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables.
HSF-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.
HSF-LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.
Expressions and Equations
Equivalent or Not?
Unit 5 ● Lesson 12/13
Best representation
Warm-up
Page 254
Page 370
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 5 ● Lesson 12/13
Let’s study and compare equations and graphs of exponential functions.
We can write an equation for an exponential function so that we can use equations and graphs to compare functions.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Where were we? Where are we? Where are we going?
Unit 5 ● Lesson 12/13
Agenda Review
You are successful today when...,
● You can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
● You can use equations and graphs to compare exponential functions.
● You can explain the meaning of the intersection of the graphs of two functions in terms of the situations they represent.
● When you know two points on a graph of an exponential function, you can write an equation for the function.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Do today's duty, fight today's temptation;
do not weaken and distract yourself by looking forward to things you cannot see, and could not understand if you saw them.
Do today what should be done...Today is the pupil of yesterday. ---Charles Kingsley
Submitted by CM
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
12.2 Activity: Equations and Their Graphs
You can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
5 mins Total
Q1 only: 3 mins group - 2 mins class share
pg 370
When b is greater than 1, larger values of b mean that the function grows more quickly as x increases. A positive value less than one of b is means the function is decreasing as x increases.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
12.3 Activity: Equations and Their Graphs
You can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
5 mins Total
Q1 only: 2 mins group - 2 mins class share
pg 371
The functions are all exponential and the bases are all less than 1 so the graphs will be decreasing. The most rapidly decreasing will be the one with the smallest base and the least rapidly decreasing will be the one with the largest base.
D
C
B
A
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
13.2 Activity: Value of A Computer
You can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
15 mins Total
2 Questions: 4 mins individual - 3 mins group - 3 mins class share
pg 377
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
13.2 Activity: Value of A Computer
You can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
$400
𝒇(1) = 200
The value of the computer at 1 year
The computer loses half of its value each year.
𝒇(x) = 400(1/2)ˣ
NO
The key is to notice that every 2 years, the computer's value is multiplied by ¼. This means that the annual decay factor is ½, since √¼ = ½. (The 4th root of 25/400, or 0.625, is also ½.)
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
13.2 Activity: Value of A Computer
You can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
13.2 Activity: Value of A Computer
You can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
The factor of growth or decay and the initial value
The x coordinates (inputs) of first two points differ by 1.
Vertical- intercept
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
13.3 Activity: Moldy Wall
You can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
10 mins Total
3 mins individual - 2 mins group - 3 mins class share
pg 379
Mold A = dashed curve, Mold B = solid curve
Mold A
At p months there was the same amount of Mold A and Mold B on the wall (q square inches), after which Mold B started to have larger area than Mold A.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Reasoning about Exponential Graphs
You can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
1
2
Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Two Graphs
You can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
The same number of followers
8
Cool-down
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 5 ● Lesson 12/13
● I can describe the effect of changing a & b on a graph that represents 𝒇(x) = a ⦁ bˣ.
● I can use equations and graphs to compare exponential functions.
● I can explain the meaning of the intersection of the graphs of two functions in terms of the situations they represent.
● When I know two points on a graph of an exponential function, I can write an equation for the function.
Learning
Targets
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Glossary
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.