Problems

If you need graph paper for these problems, click on the image at the right to open a page from which you can print. Start each graphing problem by labeling and scaling your axes in a way that is reasonable for that problem.

For each of the relationships in Exercises 1 – 16 :

1. Identify the two quantities that vary, and decide which should be represented by an independent variable and which by a dependent variable.
2. Sketch a reasonable graph to show a possible relationship between the two variables. (You should be concerned only with the basic shape of the graph, not with particular points.)
3. Write a sentence or two to justify the shape and behavior of your graph.

1. The height of a baseball after being hit into the air.
2. The speed of an egg dropped from the tenth floor of a building.
3. The height of an individual as he or she ages.
4. The amount of time it takes a person to run a mile as he or she ages.
5. The amount of money in a savings account over an extended period of time.
6. The size of a person's vocabulary from birth onwards.
7. The number of bacteria in a laboratory culture over a period of time.
8. The daily high temperature at your local airport over a calendar year.
9. The number of students absent from class and the day of the academic year.
10. The temperature of an ice-cold drink left in a warm room over a period of time.
11. The number of hours of daylight and the day of the year.
12. The cost of a pizza and the diameter of the pizza.
13. A safe following distance for your car at a given speed.
14. Ideal weight at a given height, as represented by a chart in your doctor's office.
15. The income tax on a given taxable income.
16. The sales tax on a given purchase.
17. 
    

    Table P1   Parcel Post Local Rates

    Weight Not Over (pounds)	1	2	3	4	5	6	7	8	9	10
    Postage ($)	4.38	4.72	5.05	5.35	5.63	5.88	6.02	6.12	6.23	6.33

    1. Sketch a graph of the relationship in Table P1. (You may have done this already.)
    2. Identify dependent and independent variables.
    3. Discuss any conclusions you can draw from the shape of your graph.
       
18. 
    

    Table P2   Federal Income Tax for a Single Status Filer

    If taxable income is  over--	But not over--	The tax is:
    $0	$7,550	10% of the amount over $0
    $7,550	$30,650	$755 plus 15% of the amount over 7,550
    $30,650	$74,200	$4,220.00 plus 25% of the amount over 30,650
    $74,200	$154,800	$15,107.50 plus 28% of the amount over 74,200
    $154,800	$336,550	$37,675.50 plus 33% of the amount over 154,800
    $336,550	no limit	$97,653.00 plus 35% of the amount over 336,550

    1. Sketch a graph of the relationship in Table P2.
    2. Identify dependent and independent variables.
    3. Discuss any conclusions you can draw from the shape of your graph.