MATH 133 AIU Graphing Graphs of Math Equations Questions

+MATH133 – Unit 1 Point Values:Question
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MATH133 – Unit 1 Individual Project
NAME (Required): ____DeMario Adams_______________
Assignment Instructions:
1. For each question, show all of your work for full credit.
2. Insert all labeled and titled graphs by using screenshots from Excel or desmos.com as
described in the Unit 1 Discussion Board (or other graph program).
3. Provide final answers to all questions in boxes provided.
4. Round all value answers to 3 decimal places, unless otherwise noted.
Formulas and Equations
You will use the following formulas and equations for this assignment. Linear equations are in
either point-slope form or slope-intercept form.
Point-slope form:
𝒚 − 𝒚𝟏 = 𝒎(𝒙 − 𝒙𝟏 )
Slope-intercept form: 𝒚 = 𝒎𝒙 + 𝒃
Where:
•
m is the slope of the line
•
𝑠𝑙𝑜𝑝𝑒 = 𝑚 = (𝑥2−𝑥1)
•
•
𝑏 is the y-intercept of the function’s graph
(𝑥1 , 𝑦1 ) represents some point on the line
(𝑦 −𝑦 )
2
1
Use the following scenario for Questions 1 through 4:
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The information technology department found data irregularities in the transaction rate of a
server. Your supervisor asked you to analyze the data to find the linear equation that best
represents these rates, to compare the predicted transaction rate to the questionable data.
Observations suggest that this server can store 𝑦 megabits of data in 𝑥 microseconds (see Table
A).
First Letter of Your
𝑥1
𝑦1
𝑥2
𝑦2
(microseconds) (megabits) (microseconds) (megabits)
Last Name
A–D
15 to 16.99
12.5 to 12.99
17 to 19.99
17.5 to 17.99
E–H
20 to 21.99
13.5 to 13.99
22 to 24.99
18.5 to 18.99
I–L
25 to 26.99
14.5 to 14.99
27 to 29.99
19.5 to 19.99
M–P
30 to 31.99
15.5 to 15.99
32 to 34.99
20.5 to 20.99
Q–T
35 to 36.99
16.5 to 16.99
37 to 39.99
21.5 to 21.99
U–Z
40 to 41.99
17.5 to 17.99
42 to 44.99
22.5 to 22.99
Table A: Observations of Bit-Storage Amounts and Times
1. Chose a number within each range provided for the x and y columns.
From Table A, use the row that matches the first letter of your last name to select one number
within each column’s specified range, creating two pairs of numbers (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ).
For example, if your last name starts with M, then you might choose the following:
(𝑥1 , 𝑦1 ) = (30.2, 15.6)
and
(𝑥2 , 𝑦2 ) = (32.5, 20.5)
In the table below, submit your two selected pairs of points based on your last name.
(10 points)
Your Chosen Points
(x1, y1)
(x2, y2)
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2. Use the two points from above to construct a linear function model. Create first the
point-slope form equation, and then convert the equation to slope-intercept form.
(20 points)
Hint: You will want to determine the slope first and then construct the point-slope form
of the equation before you convert it to the slope-intercept form.
Point-Slope Form
Round all value answers to 3 decimal
places.
Slope-Intercept Form
Round all value answers to 3 decimal
places.
Show your work below for constructing both linear function forms:
3. The number of megabits (y) in terms of microseconds (x) is given as follows:
𝑦 = 32.75𝑥 − 57.67
How many microseconds will it take for your model to store 200 megabits? (20 points)
How many microseconds?
Round all value answers to 3 decimal
places.
Show your work below using Equation Editor:
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Linear forecasting is the process of extrapolating the given function values to an independent
variable value that is not observed in the data. In this question, you are predicting or
forecasting the number of megabits that can be stored in 400 microseconds without collecting
any data at that range.
4. The number of megabits (y) in terms of microseconds (x) is given by the following
equation:
𝑦 = 32.75𝑥 − 57.67
How many megabits can be stored in 400 microseconds? (20 points)
How many megabits?
Round all value answers to 3 decimal
places.
Show your work below:
5. Laptop A and Laptop B have fully charged batteries and were used by company sales
staff while traveling until the laptops ran out of power (note that the laptops will not
operate when the battery voltage drops below 3.0). The two laptops have different
battery capacities and power consumption rates. Below are the graphs that show the
power consumption. The x-axis represents the time used (in hours), and the y-axis
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represents the remaining voltage in the battery. Using these graphs, determine which
laptop is more efficient, and support your choice using appropriate math. (30 points)
Hint: Keep in mind that what you are looking to compare is in volts per hour.
Which laptop is more
efficient?
Explain your answer below:
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