Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and...
-
Upload
ophelia-hensley -
Category
Documents
-
view
212 -
download
0
Transcript of Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and...
![Page 1: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/1.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Warm Up
1. Find the slope and y-intercept of the line that
passes through (4, 20) and (20, 24).
The population of a town is decreasing at a rate of 1.8% per year. In 1990, there were 4600 people.
2. Write an exponential decay function to model this situation.
3. Find the population in 2010.
![Page 2: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/2.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Look at the tables and graphs below. The data show two ways you have learned that variable quantities can be related. The relationship shown is linear.
![Page 3: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/3.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Look at the tables and graphs below. The data show two ways you have learned that variable quantities can be related. The relationship shown is quadratic.
![Page 4: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/4.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Look at the tables and graphs below. The data show two ways you have learned that variable quantities can be related. The relationship shown is exponential.
![Page 5: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/5.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
In the real world, people often gather data and then must decide what kind of relationship (if any) they think best describes their data.
![Page 6: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/6.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Example 1A: Graphing Data to Choose a Model
Which kind of model best describes the data?
Time(h) Bacteria
0 24
1 96
2 384
3 1536
4 6144
![Page 7: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/7.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Example 1B: Graphing Data to Choose a Model
Which kind of model best describes the data?
Boxes Reams of paper
1 10
5 50
20 200
50 500
![Page 8: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/8.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Check It Out! Example 1a
Which kind of model best describes the data?
x y
–3 0.30
–2 0.44
0 1
1 1.5
2 2.25
3 3.38
![Page 9: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/9.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Check It Out! Example 1b
Which kind of model best describes the data?
x y
–3 –14
–2 –9
–1 –6
0 –5
1 –6
2 –9
3 –14
![Page 10: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/10.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
We’re going to use our calculators to help us find models for the following data sets
![Page 11: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/11.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
We’re going to use our calculators to help us find models for the following data sets
![Page 12: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/12.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
After deciding which model best fits the data, you can write a function. Recall the general forms of linear, quadratic, and exponential functions.
![Page 13: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/13.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Time (s) Height (ft)
0 4
1 68
2 100
3 100
4 68
Height of golf ball
Determine which model best fits the dataand then find the equation for the model
![Page 14: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/14.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Determine which model best fits the dataand then find the equation for the model
Time (yr) Amount ($)
0 1000.00
1 1169.86
2 1368.67
3 1601.04
Money in CD
![Page 15: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/15.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Determine which model best fits the dataand then find the equation for the model
Data (1) Data (2)
–2 10
–1 1
0 –2
1 1
2 10
![Page 16: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/16.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Example 3: Problem-Solving Application
Use the data in the table to describe how the number of people changes. Then write a function that models the data. Use your function to predict the number of people who received the e-mail after one week.
Time (Days) Number of People Who Received the E-mail
0 8
1 56
2 392
3 2744
E-mail forwarding
![Page 17: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/17.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Use the data in the table to describe how the oven temperature is changing. Then write a function that models the data. Use your function to predict the temperature after 1 hour.
Check It Out! Example 3
![Page 18: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/18.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Lesson Quiz: Part I
Which kind of model best describes each set of data?
1. 2.
![Page 19: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/19.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Lesson Quiz: Part II
3. Use the data in the table to describe how the amount of water is changing. Then write a function that models the data. Use your function to predict the amount of water in the pool after 3 hours.
![Page 20: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/20.jpg)
Holt McDougal Algebra 1
9-4 Linear, Quadratic, and Exponential Models
Comparing Functions
![Page 21: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/21.jpg)
Holt McDougal Algebra 1
9-5 Comparing Functions
Example 2: Comparing Exponential FunctionsAn investment analyst offers two different investment options for her customers. Compare the investments by finding and interpreting the average rates of change from year 0 to year 10.
![Page 22: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/22.jpg)
Holt McDougal Algebra 1
9-5 Comparing Functions
Check It Out! Example 2
Compare the same investments’ average rates of change from year 10 to year 25.
![Page 23: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/23.jpg)
Holt McDougal Algebra 1
9-5 Comparing Functions
Students in an engineering class were given an assignment to design a parabola-shaped bridge. Suppose Rosetta uses y = –0.01x2 + 1.1x and Marco uses the plan below. Compare the two models over the interval [0, 20].
Check It Out! Example 3
![Page 24: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/24.jpg)
Holt McDougal Algebra 1
9-5 Comparing Functions
Example 4: Comparing Different Types of Functions
A town has approximately 500 homes. The town council is considering plans for future development. Plan A calls for an increase of 50 homes per year. Plan B calls for a 5% increase each year. Compare the plans.
Let x be the number of years. Let y be the number of homes. Write functions to model each plan
![Page 25: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/25.jpg)
Holt McDougal Algebra 1
9-5 Comparing Functions
Two neighboring schools use different models for anticipated growth in enrollment: School A has 850 students and predicts an increase of 100 students per year. School B also has 850students, but predicts an increase of 8% per year. Compare the models.
Check It Out! Example 4
Let x be the number of students. Let y be the total enrollment. Write functions to model each school.
![Page 26: Holt McDougal Algebra 1 9-4 Linear, Quadratic, and Exponential Models Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20)](https://reader035.fdocuments.in/reader035/viewer/2022081603/56649f2b5503460f94c46846/html5/thumbnails/26.jpg)
Holt McDougal Algebra 1
9-5 Comparing Functions
Lesson Quiz: Part III
3. A car manufacturer has 40 cars in stock. The manufacturer is considering two proposals. Proposal A recommends increasing the inventory by 12 cars per year. Proposal B recommends an 8% increase each year. Compare the proposals.