Lesson 6.4 - Exponential Functions

8/9/2019 Lesson 6.4 - Exponential Functions

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Chapter 6 ExponentialEquations and Functions

Lesson 6.4 Exponential Functions


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Start Thinking.


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TodayLearning Target: Day 1! I can identify the characteristics of an exponential function

! I can differentiate between a linear, quadratic and exponential function

Learning Target: Day 2

! I can graph an exponential function and a vertical translation

! I can write an exponential function that represents a given graph/table

!

Agenda: Day 1

! Start Thinking

! Do Now

! Activity 1

! Difference between 2x, x^2, 2^x

!

Agenda: Day 2! A Reward

! Key Idea

! Examples 1 5

! On Your Own Practice

!

Homework: # 1-3, 11-17(odd), 30, 36, 38, 40-42, 43-46 on p. 289-291 inyour textbook.


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2x, 2x, x2 look similar since they all

have the number 2 and the variablex, but they have very different

meanings. Looking at tables and

graphs for these expressions will helpyou understand just how different

they are.


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Complete the table below to compare the the expressions.

x 0 1 2 3 4 5

2x

2

x

x2

As x increases from 0 to 5, which expressions valuesincrease most quickly?


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Use your table from above to plot the points for each set ofordered pairs, (x,2x), (x, 2x) and (x, x2), on one set of

axes.

Use a different color for each set of points to help youidentify which is which. How are the graphs similar? How

are they different?


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An Example..

Many single-celled organisms reproduce by dividing into two

identical cells. Suppose an amoeba divides into two amoebasevery half hour.

a.

A biologist starts an experiment with one amoeba. Make a

table showing the number of amoebas she would have at

the end of each hour over an 8-hour period.

b.

Write an equation for the number of amoebas, a after t

hours.

c.

How many hours will it take for the number of amoebas

to reach 1 million?

d.

Make a graph of the (time, amoebas) data from part a.


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IDENTIFY AND

REASON OUT.


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Summarize

When you are graphing, make sure you include the followingValues for x = -2, -1, 0, 1, 2 and 3


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Try This


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Chapter 6 Exponential

Equations and Functions

Lesson 6.4 Exponential Functions Day 2


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REQUESTING A REWARD THE STORY

One day in the ancient kingdom of Montarek, a peasant saved the life of

the kings daughter.. The king was so grateful that he told the peasant

she could have ant reward she desired. The peasant-who was also the

kingdoms chess champion-made an unusual request.

I would like you to place one ruba on the first square of a chessboard,

2 rubas on the second square, 4 on the third, 8 on the fourth square andso on, until you have covered all 64 squares. Each square should have

twice as many rubas as the previous square.

The king replied, Rubas are the least valuable coin in the kingdom.

Surely you can think of a better reward. But the peasant insisted, sothe king agreed to her request.


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REQUESTING A REWARD ANSWER THE FOLLOWING QUESTIONS.

A.

Make table showing the number of rubas the king will place onsquares1 through 10 of the chessboard.

B. How does the number of rubas change from one square to the next?

C. How many rubas will be on square 20? On square 30? On square 64?

D. What is the first square in which the king will place at least

1 million rubas?

E. If a Montarek ruba is equivalent o a U.S. penny, what would the dollar

value of the rubas on squares 10, 20, 30, 40, 50 and 60 be?

F. Graph the (number of squares, number of rubas) data for squares 1 to

10. As the number of square increases, how does the number of rubas

change? What does this pattern of change tell you about the peasants

reward?G. Write an equation for the relationship between the number of square

n, and the number of rubas, r.


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Check your answer:


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Lesson 6.4 - Exponential Functions

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