Postage Cost Worksheet

Topics: Regression analysis, Derivative, Polynomial Pages: 10 (657 words) Published: December 15, 2014

Student Name: ____Chesey Colston ______
Date: _____12/3/2014_____ Class: Algebra 2
Explore Linear Models:

Years
of School
Average Weekly Paycheck
Some high school
11
450
High school graduate
13
585
Some college
15
810
Bachelor’s degree
17
1000
Master’s degree
19
1250
Doctoral degree
21
1600

1) Which type of function (linear, exponential, or cubic) do you believe will best fit the data? Support your choice. My choice would be a Linear Function because it doesn’t go through an intersection like an exponential function would, it also wouldn’t be a cubic function because it is not curved. It has all straight lines. 2) Find the rate of change between the data points of these intervals: (High school graduate) and (Some college)

High school graduate~ {585, 13} and some collage~ {810, 15}
M= {15-13} / {810-585}
M= 2 / 225
M= 112.5
(Some college) and (Bachelor’s degree)
Some Collage~ {810, 15} and Bachelor’s Degree~ {1000, 17}
M= {17-15} / {1000-810}
M= 2 / 190
M= 95

(Bachelor’s degree) and (Master’s degree)
Bachelor’s {1000, 17} and Masters {1250, 19}
M= {19-17} / {1250-1000}
M= 2 / 50
M= 125
3) Use linear regression (least squares or line of best-fit) to determine an equation for the data.

4) Compare the slope of the equation you just wrote with the rate of change values you calculated in step two. How are they the same or different? What do they represent?

5) Graph the equation you wrote in step four superimposed over the original data. Comment on how well or how poorly the equation fits the data.

6) Predict the amount of money you could expect to make each week based on 23 years of completed schooling. Explain how you came up with this prediction.

Explore Exponential Models:
Graph the table of data. Use your graph to answer the questions that follow. Number of Rounds
People Receiving Forward
1
2
2
4
3

4

5

6

7

8

9

10

1) Which type of function (linear, exponential, or cubic) do you believe will best fit the data? Support your choice.

2) Find the rate of change between the data points of these intervals: (Round 1) and (Round 2)

(Round 2) and (Round 3)

(Round 3) and (Round 4)

3) What do the rate of change values you just calculated represent? Describe the pattern you see in them.

4) Use exponential regression (or find a constant ratio) to determine an equation for the data.

5) Graph the equation you wrote in step four superimposed over the original data. Comment on how well or how poorly the equation fits the data.

6) If the rounds of forwarding continued in the same pattern, predict the round that would be first to end up sending the link to more than 50,000 people. Explain how you came up with this prediction.

Explore Cubic Models:
Record the volumes.
Size of Corner Cut
Volume of the Box (lwh)
1
100
2

3

4

5

Graph the table of data. Use your graph to answer the questions that follow.

1) Which type of function (linear, exponential, or cubic) do you believe will best fit the data? Support your choice.

2) Find the rate of change between the data points of these intervals: (Corner Cut 1) and (Corner Cut 2)

(Corner Cut 2) and (Corner Cut 3)

(Corner Cut 3) and (Corner Cut 4)

3) What do the rate of change values you just calculated represent? Why are some positive and some negative?

4) Use cubic regression to determine an equation for the data (or lwh where (12 – x) represents the sides and (x) represents the height of the box).

5) Graph the equation you wrote in step four superimposed over the original data. Comment on how well or how poorly the equation fits the data.

6) If the box company wanted to create even more options, they could cut corners that were half units. Predict the volume of a box made from corner cuts that are 2.5 x 2.5 in...
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