MATH 163

(Projects and Instructions)

Directions: Please pick ONEProject

Project A

A ball is thrown upward and its height measured at 0.5-second intervals using a strobe light.The resulting data are given in the table.

1.Draw a scatter plot of the data.

2.Examine the shape of the scatter plot in #1, what degree polynomial is appropriate for modeling the data? Explain your reasoning.

3.Using your graphing utility ( best fit function), find a polynomial function that models the data.

4.Provide a graph of the function found in # 3

5.Using your polynomial function in #4, calculate the maximum height attained by the ball?

6.Using your polynomial function #4, calculate the time at which the ball hits the ground.

7.What is the appropriate domain and range of this model? Explain the meaning of domain and range using the informationprovided in this problem.

Time (s)

Height (ft)

0

4.2

0.5

26.1

1.0

40.1

1.5

46.0

2.0

43.9

2.5

33.7

3.0

15.8

Project B

A firefighter holds a hose 4m off the ground and directs a stream of water towards a burning building.The water leaves the hose at an initial speed of 20 m/sec at an angle of 30 degrees. The height of the water can be approximated by h(x) = - 0.026x2 + 0.577 + 4, where h(x) is the height of the water in meters at a point x meters horizontally from the firefighter to the building.

1.Draw a scatter plot of your data

2.In a separate graph, connect the points of your scatter plot

3.Looking at your graph, what kind of function best fits your data? Explain your reasoning.

4.Determine the distance from the firefighter at which the maximum height of the water occurs. Round to the nearest tenth.

5.What is the maximum height of the water? Round to the nearest tenth.

6.The flow of the water follows a certain shape.Using this information, what is the distance from the firefighter to where the water hits the ground?

7.Find the domain and range of the function that models this problem. Explain your answer based on the information in this problem.

Project C

Time (s)

Volume (L)

0

0.00

0.5

0.11

1.0

0.29

1.5

0.47

2.0

0.63

2.5

0.76

3.0

0.812

3.5

0.75

4.0

0.56

4.5

0.20

The volume(in liters) of air in the lungs during a 4.5 sec respiratory cycle is shown in the table below.

1.Draw a scatter plot of the data

2.Connect the points of the scatter plot.

3.What polynomial does it resembles? What is the degree of this polynomial?

4.Using your graphing utility, find the polynomial function that models the volume.

5.Find the end behavior of this function

6.Looking at the interval given on the table for time, does this polynomial equation have maxima or minima? If yes, find the one that applies. If not, explain why?

7.Find the domain and range

8.Using the information given in this problem, how can you describe the domain and range?

Project Write Up

Please READ this carefully!!

***Must use PowerPoint Presentation or any other software that is appropriate for presentations.

*** Between 6 -10 slides

***Be creative J

*** Audio portion of the presentation must be added to the presentation ( not a separate file)

PowerPoint Presentation should include:

Title page (Create a Title, graphic or design as background related to your title)- 1 slide

Introduction ( Minimum of 5 sentences)- 1 slide

Body (labeled tables and graphs, critical steps and final answers must be shown)- 3 to 7 slides

Conclusion (summarize your findings in a paragraph)- 1 slide

Grade (out of 100 points)

10 points for Title page give title name

10 points for Introduction

50 points for Body

20 points for Conclusion

10 points for quality/creativity (animations, visually appealing, quality of presentation, sentence structure etc..)

NOTE:

This project should take you at most 1 day (24 hrs) to complete. The project is due on BRIGHTSPACE by August 13^th 11:59 pm

Late projects will not be accepted. Projects received after the due date via email will not be accepted.