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Algebra 2 7-1 Complete Lesson: Exploring Exponential Models

Last updated almost 4 years ago
35 questions
Note from the author:
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.
10

Solve It! You are to move the stack of 5 rings to another post.
Here are the rules:
â—† A move must consist of taking the top ring from one post and placing it onto another post.
â—† You can move only one ring at a time.
â—† 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
30

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.

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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.

10

Problem 2 Got It?

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Problem 2 Got It?

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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?

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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?

10

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?

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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.

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

10

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

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10
10
30

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.
30

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.
10
10

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

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

10

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

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

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

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

10

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

20

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.

10

Review Lesson 4-4: Factor the expression completely.

30

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.

10

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

10

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

10

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

10

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

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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
100

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.

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Reflection: Math Success