# 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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