For this assignment you don’t have to record yourself, just record the paper and do the work on the paper, make sure the audio is not muted, thank you very much for all your help!!
For this assignment you don’t have to record yourself, just record the paper and do the work on the paper, make sure the audio is not muted, thank you very much for all your help!!
Project Objectives:
• Create a mathematical model given data that’s represented graphically.
• Create a video presentation covering in detail how the model is created.
• Solve an applied problem related to the concept of limits.
• Create a video presentation covering in detail how the applied problem is solved.
Assessment Criteria:
The projects assess two general areas: knowledge of business calculus concepts as they apply to real life problems AND soft skills such as effective communication and time management skills. Your knowledge and understanding are assessed based on your explanation and presentation provided in the recorded video clip.
Let’s get started!
For this project create a single video presentation. In the video presentation you will cover the two tasks given below. First read and complete Steps #1 and #2 for each task (in these steps you will prepare and gather all the information and calculations that are needed for your video presentation), then complete Step #3 of these tasks which is to create the video presentation that covers Task #1 and Task #2.
Task #1
Purpose: Create a mathematical model (in this case a piece-wise function) to represent a real-life event (in this case the GDP swings in US between the years of 1929 and 1938).
Step #1
First watch the short video given below to learn about GDP. https://youtu.be/iLom1WlqwS0?si=5XpOZlAB19zeK9h_
Step #2 Gather all the necessary information and mathematical computations before you start recording your video presentation.
◦ Educate yourself about the GDP swings in the US between 1929 and 1938 based on the real events. You will be asked to talk about this in your video (not read from scripts, but rather talk about it)
◦ Create a piece-wise function that could model the GDP curve given below. This involves multiple steps and calculations, so do all the work on a piece of paper and rehearse. You will be asked to teach step-by-step how to create the piece-wise function in your video.
◦ To create the piece-wise function break the curve given below into pieces (here’s a suggestion: consider the following time intervals, note that we have let year 1929 be represented by x=0
you want to do the same, otherwise, your equations will be incorrect (for example, they will show an incorrect y-intercept). (0 ◦ Work out all the details on your paper as you create the piece-wise function. Remember you are going to teach your audience how to create the piece-wise model. So, you need to learn how to do it first to be able to teach it to someone else. When you teach, you are expected to explain each piece. For linear pieces, you need to explain how someone goes about writing a linear equation given two distinct points. For the parabolic piece, you need to explain how one goes about creating a quadratic function given the vertex and another point on the parabola using the vertex form.
◦ Identify the domain for your piece-wise function.
Accessible image attributes: GDP graph shown in above image is to be used to create the piece-wise model. Within points (1929,1050) and (1932,750) graph is a decreasing line; from (1932,750) to (1935,1000) an increasing line; between (1935,1000) and (1937,1000) a downward parabola having a vertex at (1936,1100); an increasing line from (1937,1000) to (1938, 1350).
Step #3 Now you are ready to start creating your video presentation for the first task.
◦ In your video presentation first introduce yourself, I need to see who is presenting.
◦ In your video presentation discuss very briefly the GDP swings in the US between 1929 and 1938 in accordance with the given GDP graph. Were there any events or circumstances conspiring these swings? Do not read from script, use your own words to explain what you know about these events. Reference any sites or sources you have utilized to obtain the information.
◦ In your video presentation teach us how to construct the piece-wise function step-by-step. How did you decide on the type of function for a given portion (Linear vs. Non-Linear), did the shape of the graph help you made this decision? How did you construct a linear function? What type of a non-linear function did you use in your piece-wise function and why? How did you construct your non-linear function? What is the domain for each piece?
Task #2
Purpose: Apply the concept of the limit to solve a business-related problem.
Step #1 First watch the following video to learn about the economies of scale.
Step #2 Gather all the necessary information and mathematical computations before you start recording your video presentation.
◦ Answer all five questions given below and register your response in your notebook (or a piece of paper) and rehearse.
Question #1) A company manufactures surfboards. Give an example of a fixed cost and a variable cost related to the manufacturing of the boards. (These are non-numerical examples, here’s an example: a variable cost could be cost of material used for the boards which could vary based on the changing price of the material)
Question #2) The graph below shows the average total cost per surfboard,
C
¯
¯
¯
¯
(x)
, for an output of
x
surfboards for the company. What does average total cost imply? How does it differ from the total cost,
C(x)
?
Question #3) What is the limit of the average total cost function as production increases significantly?
Question #4) Does the graph suggest that the average total cost of producing a surfboard will equal to $0 when the company manufactures a large number of boards?
Question #5) Does the graph suggest that the company achieves economies of scale by increasing production significantly?
Step #3 Now you are ready to start creating your video presentation.
◦ In your video presentation explain and talk about all five questions that you answered above. Remember not to read from script!
Video Presentation Requirements:
• Video presentation should not exceed 30 minutes.
• Introduce yourself in the beginning of the video presentation (I need to know who is presenting, I need to see your face (at least during the introduction))
• All submissions including video clips should be professional and adhere to Mission college’s student code of conduct. Review your video presentation carefully before submitting.
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