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Algebra 2 7-1 Complete Lesson: Exploring Exponential Models

Last updated over 4 years ago

35 questions

Note from the author:

10

A.CED.2

30

F.IF.7.e

10

F.IF.7.e

10

A.CED.2

10

A.CED.2

30

F.IF.7.e

30

F.IF.7.e

10

A.SSE.1.b

10

A.SSE.1.b

10

A.SSE.1.b

10

A.SSE.1.b

10

A.SSE.1.b

10

A.SSE.1.b

10

F.IF.7.b

10

F.IF.7.b

20

F.IF.7.b

10

F.IF.8.a

30

A.REI.8

10

F.IF.7.e

10

10

10

A.SSE.1.b

10

A.SSE.1.b

100

10

A.CED.2

A.SSE.1.b

F.IF.7.e

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Question 1

1.

Question 2

2.

Problem 1 Got It? Graph the functions in the same coordinate plane using contrasting colors. Include all relevant graph detail and label the functions.
Graph the functions by hand first, but you may check your graphs with Desmos and make edits as needed.

Question 3

3.

10

F.IF.7.e

10

F.IF.7.e

10

F.IF.7.e

10

A.CED.2

Question 8

8.

Question 9

9.

10

10

F.IF.7.e

10

A.SSE.1.b

10

A.SSE.1.b

10

A.SSE.1.b

10

A.SSE.1.b

Question 16

16.

a. Sketch the function on the canvas below by hand using the blue pen tool
b. Graph the function on the embedded Desmos graphing calculator above
c. Sketch a copy of the Desmos graph below using the red pen tool on the same plane as your blue sketch (it is okay if your graphs overlap, that's good!)

Be sure to include important graph detail: label axes and indicate the scale of each axis.

Question 17

17.

a. Sketch the function on the canvas below by hand using the blue pen tool
b. Graph the function on the embedded Desmos graphing calculator above
c. Sketch a copy of the Desmos graph below using the red pen tool on the same plane as your blue sketch (it is okay if your graphs overlap, that's good!)

Be sure to include important graph detail: label axes and indicate the scale of each axis.

Question 19

19.

Question 20

20.

Question 21

21.

Question 22

22.

Question 23

23.

Error Analysis: A classmate says that the function shown has a growth factor of 0.3. What is the student's mistake?

Question 24

24.

Review Lesson 6-8: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

Question 25

25.

Review Lesson 6-8: Graph the function. Zoom and pan your graph to establish an appropriate viewing window.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

Question 26

26.

Review Lesson 6-8: Graph the function on the canvas. Consider creating a table of values or translating the parent function. Include relevant graph detail.

Question 27

27.

Review Lesson 4-4: Factor the expression completely.

Question 28

28.

Review Lesson 3-6: Solve the system of equations using a matrix. Matrix frame rectangles have been added to the canvas for your convenience, along with a some matrix elements in blue. Complete your work using contrasting colors.

Question 29

29.

Review Lesson 7-1: Graph each function in the same plane. Zoom and pan your graph to establish an appropriate viewing window.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

Question 30

30.

Question 31

31.

Question 32

32.

Question 33

33.

Question 34

34.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Question 35

35.

Reflection: Math Success

Solve It! You are to move the stack of 5 rings to another post. 
Here are the rules:
◆ A move must consist of taking the top ring from one post and placing it onto another post.
◆ You can move only one ring at a time.
◆ Do not place a ring on top of a smaller ring.

Consider the fewest number of moves needed to solve pyramids composed of 1, 2, 3... rings. Match the correct minimum number of moves on the left with each pyramid described on the right.

Hint: Consider modeling the scenario with an equation in the following format: 
where m = number of moves, n = number of rings, and a and b are constants. 

1 move

2 moves

3 moves

5 moves

10 moves

31 moves

42 moves

1023 moves

1,048,575 moves

2,531,703 moves

Pyramid with 1 ring

Pyramid with 2 rings

Pyramid with 5 rings

 Pyramid with 10 rings 

 Pyramid with 20 rings 

Problem 1 Got It? Reasoning: What generalization(s) can you make about the domain, range, and y-intercepts of these functions? Select all that apply.

Domain: all real numbers

Range: all real numbers

y-intercept (0, a), where y = abx

Range: x < -1

Range: y > 0

Question 4

4.

Question 5

5.

Question 6

6.

Question 7

7.

Problem 4 Got It? Suppose you invest $500 in a savings account that pays 3.5% annual interest. When will the account contain at least $650?

After 2 years

After 3 years

After 5 years

After 8 years

After 10 years

Problem 4 Got It? Reasoning: Use the table in Problem 4 (provided again below) to determine when that account will contain at least $1650. Explain. 

After 13 years the account will contain $1710.34.

After 11 years the account will contain $1710.34.

After 8 years the account will contain $1477.50.

Question 10

10.

Question 11

11.

Question 12

12.

Question 13

13.

Question 14

14.

Question 15

15.

Reasoning: Identify the function as linear, quadratic, or exponential.

Exponential

Linear

Quadratic

Reasoning: Identify the function as linear, quadratic, or exponential.

Linear

Exponential

Quadratic

Reasoning: Identify the function as linear, quadratic, or exponential.

Exponential

Linear

Quadratic

Reasoning: Identify the function as linear, quadratic, or exponential.

Linear

Quadratic

Exponential

Vocabulary Review: Identify the expressions that are NOT powers. Select all that apply.

Vocabular Review: Match the number(s) on the left with the expression(s) on the right that contain them as exponents.

Use Your Vocabulary: Identify the equations that represent exponential decay. Select all that apply.

Use Your Vocabulary: Use an appropriate number from the left to fill in each blank on the right and create equations representing exponential decay.

0.98

7.1

Problem 2 Got It?

A

B

C

D

Problem 2 Got It?

A

B

C

D

Problem 2 Got It? You put $2000 into a college savings account for four years. The account pays 6% interest annually. Is this situation an example of exponential growth or decay? What is the y-intercept?

A

B

C

D

Problem 3 Got It? Suppose you invest $500 in a savings account that pays 3.5% annual interest. How much will be in the account after five years?

A

B

C

D

Problem 5 Got It? For the model in Problem 5, what will the world population of liberian lynx in 2020?

≈ 5

≈ 3

≈ 1

≈ 12

Problem 5 Got It? Reasoning: If you graphed the model in Problem 5, would it ever cross the x-axis? Explain.

Yes; the function has an x-intercept near 2031.

Yes; the function has an x-intercept near 2052.

No; the function is asymptotic to the x-axis. It gets closer and closer indefinitely, but never intersects the axis.

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D