ISP 120 - Quantitative Reasoning
Group Activity 9: Linear Functions
All group activities must include a signed statement from each group member that they participated fully in the assignment.
Please do the following at the beginning of every computer activity.
a. Open a new Word/Writer document.
b. Click on the "File" on the top menu bar, then go to "Save As". Give your document a somewhat descriptive name (e.g. "Group Activity 9"). Also save the document to the desktop by setting the "Save in" textbox to "Desktop". (Saving to the desktop makes it easy to retrieve your work when you are finished.)
Learning Goals for this Activity
1. Determine if each of the following tables represents a linear relationship. If it is linear, express the relationship as an equation. For your convenience, these tables can be found the in Excel file LinearOrNonlinear_2004.xls Each table is on a separate sheet within this file; click on the worksheet tabs on the bottom of the window to display each one in turn.
a.
Median Height of Children |
|
| Age (years) | Median Height (inches) |
| 2 | 35.0 |
| 3 | 37.5 |
| 4 | 40.0 |
| 5 | 42.5 |
| 6 | 45.0 |
b.
Newton's Second Law of Motion |
|
| Mass (in kilograms) | Force (in newtons) required to accelerate object at 5m/s2 |
| 1.0 | 5.0 |
| 1.3 | 6.5 |
| 1.9 | 9.5 |
| 2.2 | 11.0 |
| 3.1 | 15.5 |
c.
2004 US Income Tax (Filing Individually) |
|
|
Adjusted Gross Income ($) |
Tax ($) |
| 10,000 | 206 |
| 20,000 | 1,454 |
| 30,000 | 2,954 |
| 40,000 | 4,756 |
| 50,000 | 7,256 |
| 60,000 | 9,756 |
| 70,000 | 12,256 |
| 80,000 | 14,808 |
| 90,000 | 17,608 |
| 100,000 | 20,408 |
2. Illinois income tax is calculated based on a flat rate scale. Based on the Illinois Department of Revenue 2004 From IL-1040, listed below are tax amounts owed based on total income for a person filing individually. This file can also be found under LinearOrNonlinear_2004.xls. The worksheet is titled IL Income Tax.
2004 Illinois Income Tax (Filing Individually) |
|
| Total Income ($) | Tax ($) |
| 2,000 | 0 |
| 10,000 | 240 |
| 30,000 | 840 |
| 60,000 | 1,740 |
a. Explain why the above data represents a linear relationship.
b. Find a linear model to represent the above data and type it in your Word/Writer document.
c. What is the rate of change for this relationship? Therefore, what percent of your taxable income do you pay for Illinois state tax?
d. What is the exemption amount? (This is the amount of income that a person does not have to pay taxes on. It is also the "y-intercept" amount.)
e. How much tax to you pay if you earned less than $2,000 in a 2004?
f. Define the domain, or input values, that will work with this equation?
3. Stores such as Sam's Club and Price-Costco charge an annual membership fee of approximately $40. As a member you can purchase products at lower prices, but typically in larger quantities than one buys at ordinary stores. Savings vary from product to product, but for this question, let us assume you can save $20 for every $100 dollars you spend at one of these stores compared to shopping elsewhere.
a. Suppose you spend $100 dollars in one year at such a store. Do you come out ahead? How much do you save (or lose?) compared to not having membership and paying full price?
b. Create a table in your spreadsheet (Excel or Calc) showing the amount you spend in the first column with the corresponding overall savings in the second column. In the spend column, start with zero dollars and go up to $600 in increments of $100. Paste the completed table in your Word/Writer document.c. How much do you have to spend at the store for it to be worthwhile for you to buy membership?
d. The amount you save (or lose) by buying membership is a linear function of how much you spend. Explain why.
e. What are the two variables in this function? Assign each variable a letter. Write the linear equation for your savings as a function of how much you spend at the store.
f. What factors should you consider when deciding whether to become a member of Sam's Club or Price-Costco?