Integrated Algebra · Chapter 11-3 (Day 1): SWBAT: Solve problems involving exponential growth, exponential decay. ... Multiply, Divide, and simplify radical expressions Pgs: 32 –

Integrated Algebra

Chapter 11: Exponential Functions & Radicals

Name:______________________________

Teacher:____________________________

Pd: _______

Table of Contents

Chapter 11-3 (Day 1): SWBAT: Solve problems involving exponential growth,

exponential decay.

Pgs: 3 – 8

HW: Pgs 9-11

Chapter 11-3 (Day 2): SWBAT: Solve problems involving exponential growth,

exponential decay and half-life.

Pgs: 12 – 16

HW: Pg 17

Chapter 11-6 & 11-7 (Day 3): SWBAT: Add, Subtract and simplify radical

expressions Pgs: 18 - 22

HW: Pgs 23 – 24

Chapter 11 – 6 & 11-8 (Day 4): SWBAT: Multiply and Divide radical expressions

Pgs: 25 – 30

HW: Pg 31

Review: SWBAT Solve problems involving exponential growth, exponential decay. SWBAT Add, Subtract, Multiply, Divide, and simplify radical expressions Pgs: 32 – 39

o CHAPTER 11 EXAM

3

Day 1: Exponential Growth and Exponential Decay

SWBAT: Solve problems involving exponential growth, exponential decay

Warm-up:

Exponential growth occurs when a quantity increases by the same rate r in each period t.

When this happens, the value of the quantity at any given time can be calculated as a function of

the rate and the original amount.

Exponential decay occurs when a quantity decreases by the same rate r in each time period t.

Just like exponential growth, the value of the quantity at any given time can be calculated by

using the rate and the original amount.

Explain:

4

Example 1:

The original value of a painting is $9,000 and the value increases by 7% each year. Write an exponential growth

function to model this situation. Then find the painting’s value in 15 years.

Example 2: The population of a town is decreasing at a rate of 3% per year. In 2000 there were 1700 people. Write an

exponential decay function to model this situation, and then find the population in 2012.

Practice:

1) A sculpture is increasing in value at a rate of 8% per year, and its value in 2000 was $1200. Write an

exponential growth function to model this situation, and then find the sculpture’s value in 2006.

Answer: ______________

Step 1: Write the exponential growth function for this situation

Step 2: Find the value in 15 years.


Step 2: Find the value in 2006.

y = _________ ( 1 ______ ) ____

y = _________ ( _____ ) ____

y = _________ ( 1 ______ ) ____

y = _________ ( _____ ) ____

Step 1 Write the exponential decay function for this situation

Step 2 Find the value in 12 years.

y = _________ ( 1 ______ ) ____

y = _________ ( _____ ) ____

5

2) The number of employees at a certain company is 1440 and is increasing at a rate of 1.5% per year.

Write an exponential growth function to model this situation. Then find the number of employees in the

company after 9 years.

Answer: ______________ employees

3) The fish population in a local stream is decreasing at a rate of 3% per year. The original population was

48,000. Write an exponential decay function to model this situation. Then find the population after

7 years.

Answer: ______________

4) The deer population of a game preserve is decreasing by 2% per year. The original population was 1850.

Write an exponential decay function to model the situation. Then find the population after 4 years.

Answer: ______________




Step 2: Find the number of employees in the company after 9 years.

.

y = __________ ( 1 ______ ) ____

y = __________ ( _____ ) ____

y = ____________ ( 1 ______ ) ____

y = _____________ ( _____ ) ____


y = _______ ( 1 ______ ) ____

y = _______ ( _____ ) ____


6

Regents Questions:

Example 3: A realtor estimates that a certain new house worth $500,000 will gain value at a rate of 6% per

year since 2009. Make a table of values to approximate the number of years it will take the house to gain a

value of 3 million dollars.

What is the real-world meaning of year 0?

Which type of model best represents the data in your table? Explain. Write a function for the data.

Example 4:

Use the information in the table to predict the number of termites in the termite colony after one year.

Termite Colony Population

Time (months) Number of Termites

0 20

1 80

2 320

3 1,280

1) 5,120 termites 3) 16,777,216 termites

2) 335,544,320 termites 4) 9,920 termites

7

Example 5:

Is the equation A = 1500 (1 – 0.14)t

a model of exponential growth or exponential decay, and what is the rate

(percent) of change per time period?

1) exponential growth and 14%


3) exponential decay and 14%


Example 6:

Is the equation A = 5000 (1 + .04)t







Example 7:

The fish population of Lake Collins is decreasing at a rate of 4% per year. In 2002 there were about 1,250 fish.

Determine whether this model is an exponential growth or exponential decay, and which equation can be used

to find the population in 2008?

1) exponential growth ; y = 1250(0.96)6


3) exponential decay ; y = 1250(1.04)6


Example 8:

The value of a gold coin picturing the head of the Roman Emperor Vespasian is increasing at the rate of 5 per

year. The coin is worth $105 now. Determine whether this model is an exponential growth or exponential

decay, and which equation can be used to find what the coin will be worth in 11 years?




Explain here!

Explain here!

Explain here!

Explain here!

8

Challenge

Summary:

Exit Ticket:

1)

2) The value of a gold coin picturing the head of the Roman Emperor Marcus Aurelius is increasing at the rate

of 7 per year. If the coin is worth $145 now, what will it be worth in 14 years?

1) $308.44 3) $373.89

2) $287.10 4) $243.00

9

Homework

Write an exponential growth function to model each situation. Then find the value of the function after

the given number of years.

1)

2)

3)

Write an exponential decay function to model each situation. Then find the value of the function after

the given number of years.

4)

5)

6)

10

7) Is the equation A = 3200 (1 – 0.30)t

a model of exponential growth or exponential decay, and what is the

rate (percent) of change per time period?





8) Is the equation A = 1756 (1 + .17)

t a model of exponential growth or exponential decay, and what is the rate






9) Is the equation A = 10,000 (0.45)t







10) Is the equation A = 5400 (1.07)t







Explain here!

Explain here!

Explain here!

Explain here!

11

11)

12)

13)

Hint: Make a Table of Values

12

D a y 2 : M o r e W i t h E x p o n e n t i a l F u n c t i o n s

SWBAT: Solve problems involving exponential growth, exponential decay

Warm-Up

1) fdf 2)

1)

13

2)

3)

4)

5)

14

6)

7)

8)

9)

15

10)

11)

16

Challenge

SUMMARY

Exit Ticket

17

Day 2 – HW

4.

5.

6.

18

Day 3 - Radicals

SWBAT: Add, Subtract and simplify radical expressions

Warm – Up

QUIZ

Example 1: Simplifying Square-Root Expressions

Simplify each expression.

A. B. C.

Practice # 1


1) 2) 3)

36 49 100

19

Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400

Example 2: Simplest radical form

Simplify. All variables represent nonnegative numbers.

A. B. C.

Practice # 2


1.) 2.) 3.)

Example 3: Simplest radical form Simplify. All variables represent nonnegative numbers.

A. B.

Practice # 3 Simplify. All variables represent nonnegative numbers.

1.) 2.) 3.)

8 18

45 72

4 27 -3 20

5 28 2 75 5 8

48

80

20

Example 4: Adding and Subtracting Square-Root Expressions

Add or subtract.

Practice

Add or subtract.

Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400

Example 5: Simplify Before Adding or Subtracting


A. B.

Practice

Add or subtract.

A. B.

A.

a. b.

21

Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400

Example 6: Simplify Before Adding and Subtracting


A. B.

Practice

Add or Subtract.

A. B. C.

Challenge Problem:

Find the perimeter of the triangle. Give the answer as a radical expression in simplest form.

22

Summary:

Exit Ticket:

23

Homework


1.) 2.) 3.)

4.) 5.) 6.)

7.) 8.) 9.)

10.) 11.) 12.)

13.) 14.) 15.)

-3 98

81 180

125 52 + 56

169

2 12

4 24 20

27 3 45 28

48 2 32 18

24

Use addition or subtraction to combine the following square roots that have the same radicands.

16. 3 10 9 10 17. 8 5 3 5 18. 14 7 7 7

For problems 19 through 27, combine each of the following expressions by first simplifying the square roots

and then combining like radicands. Express each answer in simplest radical form.

19. 8 5 2 20. 3 18 4 2 21. 3 20 2 45

22. 28 5 7 23. 2 54 7 24 24. 50 200

25. 7 45 80 26. 48 27 27. 200 2 18

25

Day 4: (Multiplying and Dividing Radicals)

SWBAT: Multiply and Divide radical expressions

Warm-Up 1) 2) Simplify.

26

Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400

Section 1: Simplifying Radical Review

a) √ b) √

Section 2: Adding and Subtracting Radicals

√ + √ d) √ √

e) Gfg f)

DIVIDING RADICALS

Example 1: Using the Quotient Property of Square Roots


A) B)

27

Practice: Using the Quotient Property of Square Roots


1. 2.

Dividing Radical Expressions

Example 2: Using the Quotient Property of Square Roots


A) B) C)

Practice: Using the Quotient Property of Square Roots


1. 2. 3.

32

124

33

9615

When dividing radicals, you must divide the numbers outside the radicals and then

divide the numbers inside the radicals.

28

Multiplying Radical Expressions

Example 3: Multiplying Square Roots

Multiply. Write the product in simplest form.

Practice

Multiply. Write the product in simplest form.

Example 4: Using the Distributive Property

Multiply. Write each product in simplest form.

A. B.

A. B.

A.

When multiplying radicals, you must multiply the numbers outside the radicals and

then multiply the numbers inside the radicals.

29

Practice


Challenge Problem: Multiply. Write the product in simplest form.

Summary:

A. 10624

5354

30

SUMMARY….CONTINUED

Exit Ticket:

31

Homework

Simplify each radical expression.

(1) 8

32 (2)

2

98 (3)

5

245

(4) 2

100 (5)

4

72 (6)

64

20

(7) 2

80 (8)

42

203 (9)

25

1820


10) 11) 4 5 2 5 12)

13) 14) 15)

16) 17) 18)

3832 341053

32

Chapter 11 Review

33

34

35

36

Chapter 11 Review

33.

37.

34.

38.

35.

39.

36.

40.

37

Chapter 11 Review

41.

45.

42.

46.

43.

47.

44.

48.

38

Chapter 11 Review

49. Which function represents an exponential decay?

Explain your answer below.

52.

50. The value of a gold coin picturing the head of the Roman Emperor Vespasian is increasing at the rate of 5% per year. If the coin is worth $105 now, what will it be worth in 11 years?

a. $169.79 b. $160.00 c. $179.59 d. $162.75

53. The function f(x) = 300(0.85)x models the number of landlocked salmon in the lake x months after the lake was stocked. If the lake was stocked with fish in early April, which is the best estimate of the number of landlocked salmon in early July? A. 157 B. 184 C. 217 D. 255

51.

54. Use the data in the table to describe how the restaurant’s sales are changing. Then write a function that models the data. Use your function to predict the amount of sales after 8 years.

Restaurant Sales Year 0 1 2 3 Sales ($)

15,000 15,900 16,854 17,865.24

Function Rule: ____________________________ Answer: _____________________

52.

39

53.

54.

55.

56.

Documents

Integrated Algebra · Chapter 11-3 (Day 1): SWBAT: Solve problems involving exponential growth, exponential decay. ... Multiply, Divide, and simplify radical expressions Pgs: 32 –