24.1: E1.11- Exercises

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Exercises: For each of the following problems, after you have completed it on the spreadsheet, print the spreadsheet to turn it in with your homework.

Organize your work so that everything you want to print appears in Columns A-I. Material that appears to the right of that will not print on the same piece of 8.5 by 11 paper.
If you have the graph selected when you choose “Print” it will only print the graph. Since you need to show the numerical work as well as the graph for these, before you print, make sure that nothing is selected.
Never print long columns of numbers. These are only useful to view or compute with—not to read.

Part I.

Graph on the values and, on the same axes, graph .
1. Determine what range of x-values has the first formula value smaller than the second formula value. (Where is the curved graph below the straight line?)
2. Use the graph to estimate the y-value of $y=4+2{{(x-3)}^{2}}$ when $x=14$ .
Use the graph to estimate which x gives the lowest value for y when $y=4+2{{(x-3)}^{2}}$ on the values $0\le{x}\le12$ .
Use a spreadsheet to graph $y=\sqrt{12x+3}$ for input values between 0 and 6.
In the spreadsheet, put =PI() into a cell. See that it gives 3.14… with high precision.
Use a spreadsheet to compute the average of these six test grades: 72, 85, 69, 79, 92, 71. Then change the first score to 102 and see how the average updates to give a new value.
Use a spreadsheet to find the maximum of all the data values from the set of data below. Then replace the first value in the “Men” column, 67, with the number 85. Notice that the computed maximum changes to 85 as soon as you do this.
Men Women

67 62

57 55

63 59

49 68

52 42
Use copy and paste to get the data from column A in Example 17 to put into column A of a spreadsheet. Use formulas to find the average, standard deviation, maximum, and minimum of the set of values, putting the appropriate formulas into column C and labels in column D describing what the formula cell to the left is computing.
Use the STDEV function to compute the standard deviation of these grades: 72, 85, 69, 79, 92, 71 (the same values listed in Exercise 5 above).
Use the MAX and MIN formulas to compute the largest and smallest grades in Exercise 5.
Consider the formula . Make a spreadsheet to graph that formula in a more general way, as.
1. Then use it to investigate the effects of changing h on the shape and position of the graph.
2. Then use it to investigate the effects of changing k on the shape and position of the graph.
3. Then use it to investigate the effects of changing a on the shape and position of the graph.

Part II.

In 11-14, graph each of the following formulas using a spreadsheet. In 11 & 12, use input values from 0 to 20, with an increment of 1. In 13 & 14, use input values between 0 and 5, with an increment of 0.25.

11. $y=3{{\left(1+\frac{0.06}{4}\right)}^{4x}}$

12. $y=3{{x}^{1.8}}$

13. $y=\frac{12x}{4{{x}^{2}}+7}$

14. $A=\frac{5}{1+8\cdot{{3}^{t}}}$

Use the AVERAGE function to find the average of these 8 quiz scores: 7, 9, 10, 5, 8, 9, 6, 7

16. Set up a spreadsheet to calculate the standard deviation for the set of quiz grads shown to the right. Once you have the spreadsheet set up, explore the effects of the numbers on the standard deviation by making at least three changes in grades.

Report what changes you make, and what standard deviation results after each change.

Grades
74
72
90
84
86
95
97
72

17. Using the set of measurement values listed to the right:

[a] Calculate the average, standard deviation, and maximum for the set of measurement values listed to the right.

[b] Does the maximum differ from the average by more or less than the standard deviation?

Measurements
433
442
439
436
436
447
439
440
427

18. Calculate the average, standard deviation, and maximum for the set of measurement values listed to the right.

Measurements
1,330
1,344
1,365
1,337
1,322
1,327
1,347
1,342
1,325

19. Calculate the average, standard deviation, maximum, and minimum for the set of measurement values listed to the right.

Measurements
0.398
0.376
0.423
0.416
0.355
0.422
0.360
0.416
0.374
0.379
0.446

Use the SQRT function to graph $M=2+\sqrt{8x-7}$ for values of x between 1 and 12.
For Topic B. Formulas and Graphing problem in Part II about the drug dosage, use a spreadsheet to make a more comprehensive graph to estimate more accurately the time for the concentration to be reduced to 2 ml/l. Give your estimate in hours with decimals, not in hours and minutes.
For Topic B. Formulas and Graphing problem in Part II about the landing speed, use a spreadsheet to make a more comprehensive graph in the appropriate part of the graph to estimate the weight which will have a landing speed of 100 ft/sec. to the nearest hundred pounds.
For Topic B. Formulas and Graphing problem in Part II about the logistic formula, use a spreadsheet to make a more comprehensive graph in the appropriate part of the graph to estimate the time when the value of P will be 900.
For Topic B. Formulas and Graphing problem in Part II about the break-even point, use a spreadsheet to make a more comprehensive graph so that you can estimate the break-even point to the nearest hundred thermometers.
Consider the formula $y=2{{(1.5)}^{x}}$ . Make a spreadsheet to graph that exponential formula in a more general way, as $y=a{{(b)}^{x}}$ for values of x between -6 and 6. Use that spreadsheet to investigate the effect of changing the value of the base, b, where $b>0$ . Choose some values for the base less than 1 and some greater than 1. In your solution, write a summary of what you found and give at least three graphs to support your summary.
Consider the formula $y={{x}^{2}}$ . Make a spreadsheet to graph that power formula in a more general way, as $y={{x}^{p}}$ for values of x between 0 and 6. Use that spreadsheet to investigate the effect of changing the value of p, where $0.3<p<4$ . Choose some values for the power, p, less than 1 and some greater than 1. In your solution, write a summary of what you found and give at least three graphs to support your summary.

Mathematics for Modeling. Authored by: Mary Parker and Hunter Ellinger. License: CC BY: Attribution

Men	Women
67	62
57	55
63	59
49	68
52	42