Unit 5
Exponential Situations as Functions/ Interpreting Exponential Functions
Intro to Exponential Functions
Lesson 8/9
HSN-Q.A.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
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.
HSF-IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
HSF-IF.B: Interpret functions that arise in applications in terms of the context.
HSF-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
HSF-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph linear and quadratic functions ... Graph square root, cube root, and piecewise-defined functions... Graph polynomial functions... Graph rational functions... Graph exponential and logarithmic functions...
Expressions and Equations
Equivalent or Not?
You can make sense of and describe the relationship of an exponential graph using function notation.
Correct
Warm-up
Page 254
Page 344
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 8/9
Let’s look more closely at exponential graphs and equations.
We can analyze a situation and determine whether it makes sense to connect the points on the graph that represents the situation so that we can make sense of and describe the relationship.
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 8/9
Agenda Review
You are successful today when...,
● You can analyze a situation and determine whether it makes sense to connect the points on the graph that represents the situation.
● When you see a graph of an exponential function, You can make sense of and describe the relationship using function notation.
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.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
8.2 Activity: Moldy Bread
You can make sense of and describe the relationship of an exponential graph using function notation.
10 mins Total
4 mins individual - 3 mins group - 3 mins class share
pg 337
d | A |
0 | 1 |
1 | 2 |
2 | 4 |
3 | 8 |
4 | 16 |
5 | 32 |
The area covered by mold is a function of the number of days that have passed.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
9.2 Activity: Cost of Solar Cells
You can make sense of and describe the relationship of an exponential graph using function notation.
10 mins Total
4 mins individual - 3 mins group - 3 mins class share
pg 345
5) What is the equation?
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
9.2 Activity: Cost of Solar Cells
You can make sense of and describe the relationship of an exponential graph using function notation.
1) 9 years after 1977 (or in 1986), the cost in dollars for one watt of solar energy was about $6.
2) 𝒇(4) ≈ 25 and 𝒇(3.5) ≈ 30.
These values represent the cost in dollars of one watt of solar energy in 1981 (4 years after 1977) and halfway through 1980 (3.5 years after 1977).
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
9.2 Activity: Cost of Solar Cells
You can make sense of and describe the relationship of an exponential graph using function notation.
3) 2 years after 1977 (in 1979), the cost in dollars of one watt of solar energy was 45.
5) What is the equation?
𝒇(t) = 80(0.75)ᵗ
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
9.3 Activity: Paper Folding
You can make sense of and describe the relationship of an exponential graph using function notation.
10 mins Total
4 mins individual - 3 mins group - 3 mins class share
pg 346
DESMOS
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
9.3 Activity: Paper Folding
You can make sense of and describe the relationship of an exponential graph using function notation.
The sheet of paper is 0.05 mm thick.
It takes 5 folds before the paper is more than 1 mm thick. After 4 folds the paper is 0.8 mm thick and after 5 folds it is 1.6 mm thick.
It takes 8 folds before the paper is more than 1 cm or 10 mm thick (1.28 cm to be precise).
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
9.3 Activity: Paper Folding
You can make sense of and describe the relationship of an exponential graph using function notation.
46.75, 23.375, 11.6875 square inches.
a = 93.5(½)ⁿ
Not in this situation.
No. The area of the sheet of paper can never be negative no matter how many times it is folded.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Interpreting Exponential Functions
You can make sense of and describe the relationship of an exponential graph using function notation.
Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Bacteria Population
You can make sense of and describe the relationship of an exponential graph using function notation.
622,431 days
8.7 days
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 8/9
● I can analyze a situation and determine whether it makes sense to connect the points on the graph that represents the situation.
● When I see a graph of an exponential function, I can make sense of and describe the relationship using function notation.
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.