integrated algebra - white plains public schools
TRANSCRIPT
Integrated Algebra
Chapter 11: Exponential Functions & Radicals
Name:______________________________
Teacher:____________________________
Pd: _______
Table of Contents
Chapter 11-2 (Day 1): SWBAT: Graph exponential
functions Pgs: 1 – 4
HW: 5
Chapter 11-3 (Day 2): SWBAT: Solve problems involving
exponential growth, exponential decay and half-life
Pgs: 6 – 9
HW: 10 - 11
Chapter 11-6 & 11-7 (Day 3): SWBAT: Add, Subtract
and simplify radical expressions Pgs: 12 - 16
HW: 17 – 18
Chapter 11 – 6 & 11-8 (Day 4): SWBAT: Multiply and
Divide radical expressions
Pgs: 19 – 22
HW: 23
o Chapter 11 - Practice Test: Review using E-Clickers
o CHAPTER 11 EXAM
1
Chapter 11- 2 - Graphing Exponential Functions
SWBAT: Graph exponential functions Warm – Up
Example 1: Graphing y = abx with a > 0 and b > 1
Graph: y = 0.5(2)x Practice
1) Graph: y = 2x 2) Graph: y = 0.2(5)x
2
Example 2: Graphing y = abx with a < 0 and b > 1
Practice
3) Graph y = –6x 4) Graph y = –3(3)x
3
Example 3: Graphing y = abx with 0 < b < 1 Graph: y = 4(0.6)x
Example 4: Graphing y = abx with 0 < b < 1
Graph :
4
Challenge Problem
Summary: The box summarizes the general shapes of exponential function graphs. For y = abx, if b > 1, then the For y = abx, if 0 < b < 1, then the graph will have one of these graph will have one of these shapes. shapes.
Exit Ticket
5
Homework 1) Graph: y =3x 2) Graph: y = -2(3)x 3) Graph: 4) Graph:
5. Which equation represents a quadratic function?
6
Chapter 11-3
Exponential Growth and Exponential Decay
SWBAT: Solve problems involving exponential growth, exponential decay and half – life
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.
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.
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.
Step 1 Write the exponential growth
function for this situation
Step 2 Find the value in 15 years.
Step 1 Write the exponential growth
function for this situation
Step 2 Find the value in 6 years.
7
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.
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.
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) 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.
Step 1 Write the exponential decay
function for this situation
Step 2 Find the value in 12 years.
Step 1 Write the exponential decay
function for this situation
Step 2 Find the value in 7 years.
8
2) 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.
A common application of exponential decay is half-life of a substance is the time it takes
for one-half of the substance to decay into another substance.
Example 1: Science Application
Astatine-218 has a half-life of 2 seconds. Find the amount left from a 500 gram sample of astatine-218 after 10
seconds.
Practice: Science Applications
1) Astatine-218 has a half-life of 2 seconds. Find the amount left from a 500-gram sample of astatine-218 after
30 seconds.
2) Cesium-137 has a half-life of 30 years. Find the amount of cesium-137 left from a 100 milligram sample
after 180 years.
Step 1 Find t, the number of half-
lives in the given time period.
Step 2 Set up the half-life function and
solve for the final amount.
Step 1 Find t, the number of half-
lives in the given time period.
Step 2 Set up the half-life function and
solve for the final amount.
9
Challenge Problem:
Summary:
Exit Ticket:
10
Homework
1)
Write an exponential growth function to model each situation. Then find the value of the function after
the given number of years.
2)
3)
4)
Write an exponential decay function to model each situation. Then find the value of the function after
the given number of years.
5)
6)
11
7)
8)
Solve the following half-life problems:
9)
10)
11)
12
Chapter 11 – 6 & 11 – 7 (Radicals) SWBAT: Add, Subtract and simplify radical expressions
Warm Up
Identify the perfect square in each set.
1. 45 81 27 111
2. 156 99 8 25
3. 256 84 12 1000
4. 35 216 196 72
Write each number as a product of prime numbers.
5. 36 6. 24
13
Example 1: Simplifying Square-Root Expressions
Simplify each expression.
A. B. C.
Practice # 1
Simplify each expression.
1) 2) 3)
Example 2: Simplest radical form
Simplify. All variables represent nonnegative numbers.
A. B. C.
Practice # 2
Simplify. All variables represent nonnegative numbers.
1.) 2.) 3.)
36 49 100
8 18
45 72
48
80
14
Example 3: Simplest radical form Simplify. All variables represent nonnegative numbers.
A. B.
Practice # 3 Simplify. All variables represent nonnegative numbers.
1.) 2.) 3.)
Example 4: Adding and Subtracting Square-Root Expressions
Add or subtract.
Practice
Add or subtract.
4 27 -3 20
5 28 2 75 5 8
15
Example 5: Simplify Before Adding or Subtracting
Simplify each expression.
A. B.
Practice
Add or subtract.
A. B.
Example 6: Simplify Before Adding and Subtracting
Simplify each expression.
A. B.
Practice
Add or Subtract.
A. B. C.
Challenge Problem:
16
Find the perimeter of the triangle. Give the answer as a radical expression in simplest form.
Summary:
Exit Ticket:
17
Homework
Simplify. All variables represent nonnegative numbers.
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
18
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
19
Chapter 11 – 6 & 11- 8 (Multiplying and Dividing Radicals) SWBAT: Multiply and Divide radical expressions
Warm Up
Example 1: Using the Quotient Property of Square Roots
Simplify. All variables represent nonnegative numbers.
A) B) C)
Practice: Using the Quotient Property of Square Roots
Simplify. All variables represent nonnegative numbers.
1. 2. 3.
20
Dividing Radical Expressions
Example 2: Using the Quotient Property of Square Roots
Simplify. All variables represent nonnegative numbers.
A) B) C)
Practice: Using the Quotient Property of Square Roots
Simplify. All variables represent nonnegative numbers.
1. 2. 3.
Multiplying Radical Expressions
Example 3: Multiplying Square Roots
Multiply. Write the product in simplest form.
32
124
33
9615
When multiplying radicals, you must multiply the numbers outside the radicals and
then multiply the numbers inside the radicals.
1585432
When dividing radicals, you must divide the numbers outside the radicals and then
divide the numbers inside the radicals.
6252
304
21
Practice
Multiply. Write the product in simplest form.
Example 4: Using the Distributive Property
Multiply. Write each product in simplest form.
Practice
Multiply. Write each product in simplest form.
Challenge Problem: Multiply. Write the product in simplest form.
10624
5354
22
Summary:
Exit Ticket:
23
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
Multiply. Write each product in simplest form.
10) 11) 4 5 2 5 12)
13) 14) 15)
16) 17) 18)
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