Alg2 Lesson 3.1: Problem Set for Exponential Functions

Lesson 3.1: Problem Set for

Exponential Functions

Obj: I can convert exponential models to different forms.

EQ: How do I evaluate an exponential function given
a numerical value?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

How do you plan to contribute?

• Write notes in journal

• Collaborate with peers

• Ask questions on Remind

• Complete this Quizizz

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Student Task: Complete
Handout 3.1: Exponential

Function Models

Part A

​In Part A of the handout, students use properties of exponents to develop a general rule for determining the growth or decay factor of an exponential function expressed with the natural base, e. This is a useful skill because it reinforces how to utilize properties of exponents for different problem-solving situations. Additionally, it gives students some insight into the structure and key features of exponential functions with base e.

Multiple Choice

Suppose I asked you to simplify the expression (x²)⁵. What would you do with
the exponents? I would ____ the exponents.

• add

• divide

• subtract

• multiply

Multiple Choice

What is (x⁴)^a

• 4^(ax)
• x^(4+a)
• x^(4a)
• x^(a^4)

Multiple Select

Using the power-to-a-power property of exponents which of the following are
expressions equivalent to e^3t?

• (e³)^t

• (e^t)³

• $$e^{3^t}$$

• $$e^{t^3}$$

Instructions: Be sure to show your work and/or explain your answers to the following problems.

Word Cloud

What comes to mind when you hear the word "doubling"?

Part B

In Part B of the handout, students explore the relationship between
horizontal translations and vertical dilations of exponential functions.
As in Part A, this subset of problems gives students some insight into
the structure and key features of exponential functions. Understanding that some transformations are equivalent for exponential functions will be useful in future lessons when students explore transformations of logarithmic functions.

Multiple Choice

Which of the following is equivalent to the expression x^4•x^a where a is a constant? To express this using a single base, what would you do with the exponents?

• x^(4+a)
• x^(4-a)
• x^(4a)

• x^(4/a)

Multiple Choice

Suppose I asked you to simplify the expression x^2•x^5 . To express this using a
single base, what would you do with the exponents? How do you know? I would
___ the exponents.

• add

• subtract

• multiply

• divide

Drag and Drop

How can we use the product property of exponents to rewrite e^(x+5)? Because x + 5 is a ​

Placeholder

, we could write the expression e^(x+5) as the ​

Placeholder

of two powers with the same base. This means that e^(x+5) = ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

sum

product

e^x•e^5

(5x)^e

Instructions: Be sure to show your work and/or explain your answers to the following problems.

Part C

In Part C of the handout, students investigate how to express
exponential functions using other bases. It is not necessary for students to memorize any formulas associated with changing the base of an exponential function. Rather, students should observe the adaptability of exponential function forms. This part of the handout also introduces students to the logarithm base e, or the natural logarithm. This can serve as a helpful preview of the more formal investigations they perform in later lessons.

Drag and Drop

Solve for x.

If 2^x = 5, then x = ​

Placeholder

If e^x = 5, then x = ​

Placeholder

If 10^x = 5, then x = ​

Placeholder

Drag these tiles and drop them in the correct blank above

log₂(5)

ln(5)

log(5)

Instructions: Be sure to show your work and/or explain your answers to the following problems.

Part D

Part D of the handout gives students an opportunity to use
exponential functions with base e to model contextual scenarios. These scenarios also appeared in Unit 1. You could choose to compare the models that students constructed in Unit 1 to the ones they construct here to show that they are equivalent.

Instructions: Be sure to show your work and/or explain your answers to the following problems.

https://www.desmos.com/calculator/qv5wa71eqc

Key Takeaways

Exponential Growth in a
positive direction

Exponential Growth in a
negative direction

Exponential Decay in a
positive direction

Exponential Decay in a
negative direction

Where kt > 0
As x gets larger, y goes away from the horizontal asymptote

Where kt < 0
As x gets larger, y approaches the horizontal asymptote.

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the wheel as a class and spend a minute or so
discussing our answers.