Algebra 2 7-2 Complete Lesson: Properties of Exponential Functions

Last updated over 4 years ago

25 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

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.

A.CED.2

F.IF.7.e

A.SSE.1.b

F.BF.1.b

…

A.SSE.1.b

F.IF.8.b

A.SSE.1.b

F.BF.1.b

A.CED.2

A.SSE.1.b

…

A.SSE.1.b

F.BF.1.b

F.IF.8.b

A.SSE.1.b

F.BF.1.b

F.IF.8.b

A.REI.2

A.CED.2

F.BF.4.a

G.CO.2

A.SSE.1.b

F.IF.8.b

100

A.CED.2

A.SSE.1.b

…

Algebra 2 7-2 Complete Lesson: Properties of Exponential Functions

Last updated over 4 years ago

25 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

Solve It! f and g are exponential functions with the same base.
Is the graph of g
● a compression,
● a reflection, or
● a translation
of the graph of f ? Or is it none of the above? Select all that apply.

A compression

A reflection

A translation

None of the above

A.CED.2

F.IF.7.e

Problem 1 Got It?

A.CED.2

A.SSE.1.b

…

Problem 2 Got It?

A.CED.2

A.SSE.1.b

…

Problem 2 Got It?

A.CED.2

A.SSE.1.b

…

Problem 3 Got It? Use the exponential model from Problem 3.
How long does it take for the coffee to reach a temperature of 100 degrees?

About 31.9 minutes

About 27.0 minutes

About 21.3 minutes

A.SSE.1.b

F.BF.1.b

…

Problem 3 Got It? Reasoning: In Problem 3, would the model of the exponential data be useful if you did not translate the data by 68 units? Explain.

No; a hot drink in this scenario will not cool below room temperature. In order to use exponential data, it is important to translate the data left 68 units.

No; a hot drink in this scenario will not cool below room temperature. In order to use exponential data, it is important to translate the data up 68 units.

Yes; since a hot drink in this scenario may cool well below room temperature, it is not necessary to translate the data.

A.SSE.1.b

F.IF.8.b

Problem 4 Got It? How can you use a graphing calculator to calculate e⁸?

Use the e^x key, x = 8

Graph y = e^x and find y for x = 8

Use the table of values for y = e^x and find y for x = 8

All of the above

Problem 4 Got It? Calculate e⁸. Round to 5 decimal places. Enter only a number with no commas or spaces.

Problem 5 Got It? Scholarships: Suppose you won a contest at the start of 5^th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account when you finish high school 8 years later? Express the answer to the nearest dollar.

A.CED.2

F.BF.1.b

For the function
y = -2 • 3^x, identify the transformation from the parent function
y = 3^x.

A.CED.2

A.SSE.1.b

…

For the function
y = ½(9)^x, identify the transformation from the parent function
y = 9^x.

A.CED.2

A.SSE.1.b

…

For the function
y = 7⁽^x^-5), identify the transformation from the parent function
y = 7^x.

A.CED.2

A.SSE.1.b

…

For the function
y = 5^x+ 3, identify the transformation from the parent function
y = 5^x.

A.CED.2

A.SSE.1.b

…

A.SSE.1.b

F.BF.1.b

Reasoning: Is investing $2000 in an account that pays 5% annual interest compounded continuously the same as investing $1000 at 4% and $1000 at 6%, each compounded continuously? Explain.

A.CED.2

A.SSE.1.b

…

Review Lesson 7-1: Without graphing, determine whether the function represents exponential growth or decay.

Exponential growth
Exponential decay

A.SSE.1.b

F.BF.1.b

F.IF.8.b

Review Lesson 7-1: Without graphing, find the y-intercept of each exponential function.

y-intercept: 2
y-intercept: 23
y-intercept: 3
y-intercept: 5

A.SSE.1.b

F.BF.1.b

F.IF.8.b

Review Lesson 6-3: Simplify.

A.REI.2

Review Lesson 6-3: Simplify.

A.REI.2

Review Lesson 6-3: Simplify.

A.REI.2

Review Lesson 6-7: Find the inverse of each function on the right and state whether the inverse is a function or is not a function.

f^{- -1} is a function
f ^-1 is NOT a function

A.CED.2

F.BF.4.a

Vocabulary Review: In each graph, the dashed figure is the image of the solid figure after a transformation. Categorize each transformation as a translation, reflection, or dilation.

Translation
Reflection
Dilation

G.CO.2

Use Your Vocabulary: Identify the functions that represent exponential growth. Select all that apply.

A.SSE.1.b

F.IF.8.b

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.

Reflection: Math Success

A.CED.2

A.SSE.1.b

…

Algebra 2 7-2 Complete Lesson: Properties of Exponential Functions

Algebra 2 7-2 Complete Lesson: Properties of Exponential Functions

Solve It! f and g are exponential functions with the same base.Is the graph of g● a compression,● a reflection, or● a translationof the graph of f ? Or is it none of the above? Select all that apply.

Problem 1 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? Use the exponential model from Problem 3. How long does it take for the coffee to reach a temperature of 100 degrees?

Problem 3 Got It? Reasoning: In Problem 3, would the model of the exponential data be useful if you did not translate the data by 68 units? Explain.

Problem 4 Got It? How can you use a graphing calculator to calculate e8?

Problem 4 Got It? Calculate e8. Round to 5 decimal places. Enter only a number with no commas or spaces.

Problem 5 Got It? Scholarships: Suppose you won a contest at the start of 5th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account when you finish high school 8 years later? Express the answer to the nearest dollar.

For the function y = -2 • 3x, identify the transformation from the parent functiony = 3x.

For the function y = ½(9)x, identify the transformation from the parent functiony = 9x.

For the function y = 7(x-5), identify the transformation from the parent functiony = 7x.

For the function y = 5x + 3, identify the transformation from the parent functiony = 5x.

Reasoning: Is investing $2000 in an account that pays 5% annual interest compounded continuously the same as investing $1000 at 4% and $1000 at 6%, each compounded continuously? Explain.

Review Lesson 7-1: Without graphing, determine whether the function represents exponential growth or decay.

Review Lesson 7-1: Without graphing, find the y-intercept of each exponential function.

Review Lesson 6-3: Simplify.

Review Lesson 6-3: Simplify.

Review Lesson 6-3: Simplify.

Review Lesson 6-7: Find the inverse of each function on the right and state whether the inverse is a function or is not a function.

Vocabulary Review: In each graph, the dashed figure is the image of the solid figure after a transformation. Categorize each transformation as a translation, reflection, or dilation.

Use Your Vocabulary: Identify the functions that represent exponential growth. Select all that apply.

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.

Reflection: Math Success

Solve It! f and g are exponential functions with the same base.Is the graph of g● a compression,● a reflection, or● a translationof the graph of f ? Or is it none of the above? Select all that apply.

Problem 1 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? Use the exponential model from Problem 3. How long does it take for the coffee to reach a temperature of 100 degrees?

Problem 3 Got It? Reasoning: In Problem 3, would the model of the exponential data be useful if you did not translate the data by 68 units? Explain.

Problem 4 Got It? How can you use a graphing calculator to calculate e8?

Problem 4 Got It? Calculate e8. Round to 5 decimal places. Enter only a number with no commas or spaces.

Problem 5 Got It? Scholarships: Suppose you won a contest at the start of 5th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account when you finish high school 8 years later? Express the answer to the nearest dollar.

For the function y = -2 • 3x, identify the transformation from the parent functiony = 3x.

For the function y = ½(9)x, identify the transformation from the parent functiony = 9x.

For the function y = 7(x-5), identify the transformation from the parent functiony = 7x.

For the function y = 5x + 3, identify the transformation from the parent functiony = 5x.

Reasoning: Is investing $2000 in an account that pays 5% annual interest compounded continuously the same as investing $1000 at 4% and $1000 at 6%, each compounded continuously? Explain.

Review Lesson 7-1: Without graphing, determine whether the function represents exponential growth or decay.

Review Lesson 7-1: Without graphing, find the y-intercept of each exponential function.

Review Lesson 6-3: Simplify.

Review Lesson 6-3: Simplify.

Review Lesson 6-3: Simplify.

Review Lesson 6-7: Find the inverse of each function on the right and state whether the inverse is a function or is not a function.

Vocabulary Review: In each graph, the dashed figure is the image of the solid figure after a transformation. Categorize each transformation as a translation, reflection, or dilation.

Use Your Vocabulary: Identify the functions that represent exponential growth. Select all that apply.

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.

Reflection: Math Success

Solve It! f and g are exponential functions with the same base.
Is the graph of g
● a compression,
● a reflection, or
● a translation
of the graph of f ? Or is it none of the above? Select all that apply.

Problem 3 Got It? Use the exponential model from Problem 3.
How long does it take for the coffee to reach a temperature of 100 degrees?

Problem 4 Got It? How can you use a graphing calculator to calculate e⁸?

Problem 4 Got It? Calculate e⁸. Round to 5 decimal places. Enter only a number with no commas or spaces.

Problem 5 Got It? Scholarships: Suppose you won a contest at the start of 5^th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account when you finish high school 8 years later? Express the answer to the nearest dollar.

For the function
y = -2 • 3^x, identify the transformation from the parent function
y = 3^x.

For the function
y = ½(9)^x, identify the transformation from the parent function
y = 9^x.

For the function
y = 7⁽^x^-5), identify the transformation from the parent function
y = 7^x.

For the function
y = 5^x+ 3, identify the transformation from the parent function
y = 5^x.

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.

Solve It! f and g are exponential functions with the same base.
Is the graph of g
● a compression,
● a reflection, or
● a translation
of the graph of f ? Or is it none of the above? Select all that apply.

Problem 3 Got It? Use the exponential model from Problem 3.
How long does it take for the coffee to reach a temperature of 100 degrees?

Problem 4 Got It? How can you use a graphing calculator to calculate e⁸?

Problem 4 Got It? Calculate e⁸. Round to 5 decimal places. Enter only a number with no commas or spaces.

Problem 5 Got It? Scholarships: Suppose you won a contest at the start of 5^th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account when you finish high school 8 years later? Express the answer to the nearest dollar.

For the function
y = -2 • 3^x, identify the transformation from the parent function
y = 3^x.

For the function
y = ½(9)^x, identify the transformation from the parent function
y = 9^x.

For the function
y = 7⁽^x^-5), identify the transformation from the parent function
y = 7^x.

For the function
y = 5^x+ 3, identify the transformation from the parent function
y = 5^x.

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.