Algebra 2 7-2 Guided Practice: Properties of Exponential Functions

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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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.

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Consider the exponential function f(x)=3^x.
What function stretches f(x) vertically by a factor of 2?

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Problem 1 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Consider the general form of a translated exponential function below.
What impact does a have on the graph?

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Take Note: Consider the general form of a translated exponential function below.
What impact does h have on the graph?

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Take Note: Consider the general form of a translated exponential function below.
What impact does k have on the graph?

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Take Note: Consider the exponential function f(x)=3^x.
What function translates f(x) four units to the right and two units down?

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Problem 2 Got It?

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Problem 2 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Consider the exponential function below.
Where can a negative sign be placed to cause the graph to be reflected vertically (across the x-axis)?

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Take Note: Consider the exponential function below.
Where can a negative sign be placed to cause the graph to be reflected horizontally (across the y-axis)?

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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?

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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.

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: What is the numerical value of e to the nearest hundredth? Enter only a number.

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Take Note: What is a natural base exponential function ? What can they be used to model?

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

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Problem 4 Got It? Calculate e8. Round to 5 decimal places. Enter only a number with no commas or spaces. You may use the calculators at desmos.com.

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: What is the formula for continuously compounded interest? Enter only the formula. You may use either one of the special characters \cdot or \times (that's not an x) between the P and e in your response.

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Take Note: Consider the general formula for modeling continuously compounded interest below.
What does each part of the formula represent?
Match each element in the formula with its description.

Draggable item		Corresponding Item
P		The amount in the account at time t
e		Principal - the initial amount in the account (in other words, the amount in the account at time 0)
r		An irrational constant approximately equal to 2.72
t		The annual interest rate applied to the account
A(t)		The time that interest has accrued in years

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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.

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Consider the exponential function f(x)=3^x. What function stretches f(x) vertically by a factor of 2?

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Consider the general form of a translated exponential function below.What impact does a have on the graph?

Take Note: Consider the general form of a translated exponential function below.What impact does h have on the graph?

Take Note: Consider the general form of a translated exponential function below.What impact does k have on the graph?

Take Note: Consider the exponential function f(x)=3^x. What function translates f(x) four units to the right and two units down?

Problem 2 Got It?

Problem 2 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Consider the exponential function below.Where can a negative sign be placed to cause the graph to be reflected vertically (across the x-axis)?

Take Note: Consider the exponential function below.Where can a negative sign be placed to cause the graph to be reflected horizontally (across the y-axis)?

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.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: What is the numerical value of e to the nearest hundredth? Enter only a number.

Take Note: What is a natural base exponential function ? What can they be used to model?

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. You may use the calculators at desmos.com.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: What is the formula for continuously compounded interest? Enter only the formula. You may use either one of the special characters \cdot or \times (that's not an x) between the P and e in your response.

Take Note: Consider the general formula for modeling continuously compounded interest below. What does each part of the formula represent? Match each element in the formula with its description.

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.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

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.

Take Note: Consider the exponential function f(x)=3^x.
What function stretches f(x) vertically by a factor of 2?

Take Note: Consider the general form of a translated exponential function below.
What impact does a have on the graph?

Take Note: Consider the general form of a translated exponential function below.
What impact does h have on the graph?

Take Note: Consider the general form of a translated exponential function below.
What impact does k have on the graph?

Take Note: Consider the exponential function f(x)=3^x.
What function translates f(x) four units to the right and two units down?

Take Note: Consider the exponential function below.
Where can a negative sign be placed to cause the graph to be reflected vertically (across the x-axis)?

Take Note: Consider the exponential function below.
Where can a negative sign be placed to cause the graph to be reflected horizontally (across the y-axis)?

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?

Take Note: Consider the general formula for modeling continuously compounded interest below.
What does each part of the formula represent?
Match each element in the formula with its description.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?