Fall 1999, Math 100

CHAPTER 2

Be sure to check back often, because assignments may change!

Due Friday 9/24 at 9am

Section 2.1: Introduction

• Be sure to understand: That functions can be divided into various types based on what family (or families) of functions they belong to.

Section 2.2: Linear Functions

• Be sure to understand: The Graph of a Linear Function, the ideas behind slope (formula, negative vs positive, large vs small), the point-slope form of a line, and really pay attention to the discussion of which situations call for the point-slope form and which for the slope-intercept form.

E-mail Subject Line: Math 100 Your Name 9/24

1. Find the slope of the line connecting the points (1,2) and (2,4).
2. Using the slope you found in (1), the point (1,2), and the formula for the point-slope form of the line, find the equation of the line which connects (1,2) and (2,4).
3. Find the y-coordinate of the point on this line which has x-coordinate x=-1.

Reminders:

• Remember, treat the problems sets as if they are due on Friday. This one is a group assignment. Work together, and bring questions to class on Friday. When you get in class, list the problems you have questions about on the board. If somebody else has already listed a problem that you had difficulty with, put a check next to it.

Due Monday 9/27 at 9am

Review: guidelines for homework presentation
Section 2.2: Linear Functions

• Be sure to understand: All the examples

E-mail Subject Line: Math 100 Your Name 9/27

The height of a ball is measured at several times, and the values are given below:
 t 8 10 12 14 h(t) 50 35 20 5
1. How can we quickly tell that the height and the time have a linear relationship?
2. Which variable is dependent, and which is independent?
3. What is the equation of this line?
4. When does the ball hit the ground?

Reminder:

• HW is due today at 4pm.

Due Wednesday 9/29 at 9am

Section 2.2: Linear Functions

• Be sure to understand: how to use the point-slope formula for a line, as you will need to be able to use this often and quickly; how to look at a relationship described by a chart of data and determine whether the relationship is linear.

Section 2.3: Exponential Functions

• Be sure to understand: Why the relationship between the population of Florida and time isn't linear, and why you could have predicted the graph would be concave up.

E-mail Subject Line: Math 100 Your Name 9/29

1. Use the point-slope form of the equation of a line to find the equation of the line connecting the points (2,1) and (5,-3).
2. Suppose the population of Breedonia over the course of the last several years is given below:

 yearsince 1990 0 1 2 3 4 populationin thousands 12 14.4 17.8 20.74 24.88

1. Is the relationship between population and time in Breedonia linear, exponential, or neither, or both? (I rounded to the nearest hundredth, so your answers will be somewhat approximate.)
2. Find the growth factor by which the population increases each year.
3. Find an equation which gives the population P as a function of time t.
4. Bonus:Use this equation to predict the population in the year 2010 (which is t=20).

Reminder:

• Don't forget to keep on re-taking Gateways 1 and 2 until you pass them, of course.

Due Friday 10/1 at 9am

Section 2.3: Exponential Functions

• To read: bottom of p. 62 -- middle of page 65
• Be sure to understand: Example 2 (fill in any missing details); how to get the table and graph on page 64; exponential decay; which terms are variables and which are fixed in the formula for an exponential function.

E-mail Subject Line: Math 100 Your Name 10/1

A meteorite containing an unknown radioactive element falls to Earth. (Radioactive elements decay to stable (non-radioactive) elements over time.) Scientists measure the rate of decay of this new element closely, and find that every hour, the amount of the new radioactive element still present in the meteorite decays by 13%.

1. Let Ao be the initial amount of this element. In terms of Ao, how much is left after 1 hour? After 2 hours? After 3 hours? Keep repeating this process until you are ready to:
2. Find an expression for how much (A) of the radioactive element is left after t hours.
3. Use the expression you found in (2) to determine how much of the element is left after 24 hours.
4. Estimate, as best you can, how many hours have passed when half of the original amount is left in the meteorite.

Reminder:

• Bring questions on PS 3 to class Friday, and put them up on the board.
• If you continue to have questions on PS 3, e-mail Emily Howes (our new grader/assistant) before 4pm on Sunday, and ask to meet her at 7pm in SC 120. Her e-mail address is ehowes
• The deadline for receiving 80% on Gateway 1 and 100% on Gateway 2, is Wednesday 10/6. This is because:
• Midterm 1 is 10/7. It will cover thru part of Section 2.3.
• Allow 8-10 hours for studying for this exam. Begin reviewing now. In an ideal world, reviewing consists of:
1. Re-reading all of the text, and your notes, taking notes on the main points and definitions, and looking for connections, relationships, and the big picture.
2. Some people find it valuable to recopy class notes.
3. Redoing as many assigned problems as possible, and trying some I didn't assign.
4. Doing problems from the review at the end of each chapter.
5. Doing the study guide that I'll be handing out.
• For Friday, I suggest you begin studying by making sure you've done every assigned problem, rather than only those I collect, and re-read all of the text, taking notes on the main points.
• I will give more study hints in the next reading assignment, so don't wait to read them until Monday morning!

Due Monday 10/4 at 9am

Section 2.3: Exponential Functions

• To read: middle of page 65-the end
• Be sure to understand: The difference between growth and decay factors; doubling and half-time (what they mean and how they are used); Figure 2.15.

E-mail Subject Line: Math 100 Your Name 10/4

1. Consider P(t)=15*(6t). Is 6 a growth or decay factor?
2. In P(t), what is the growth or decay rate?
3. Simplify b15/b-6.

Reminders:

• PS 3 is due by 4pm Monday.
• Remember to e-mail Emily at ehowes if you want to ask her questions Sunday at 7!
• Pass those gateways before Wednesday!
• Keep on studying: Do as many problems as possible. Don't simply look back at old problem sets; save that for when you're stuck. Make a note of those you have difficulty with, then come look at my solutions on Monday.

Due Wednesday 10/6 at 9am

Section 2.4: Power Functions

• To read: p. 74 -- middle of p. 77
• Be sure to understand: The difference between exponential functions and power functions; the shape and concavity of odd powers of x versus the shape and concavity of even powers of x; "the race to infinity"; "the race to zero".

E-mail Subject Line: Math 100 Your Name 10/6

1. For what value(s) of x does x7=x8?
2. Which power function wins "the race to infinity", y=x7 or y=x8?
3. Which power function wins "the race to zero", y=x7 or y=x8?

Reminders:

• Midterm 1 is tomorrow, 10/7. If you haven't already signed up for a time to take it, contact me!
• Do as many problems from the review sections at the end of the chapters as possible.
• Do the study guide that I handed out to you.
• Prepare your "cheat sheet": you may bring handwritten notes on one side of a standard (8 1/2 x 11) sheet of paper. You'll turn in the notes with the exam.

Due Friday 10/8 at 9am

Section 2.4: Power Functions

• To read: middle of p. 77 -- end
• Be sure to understand: the connection between roots and fractional powers; why y=x-p has a vertical asymptote at x=0, and a horizontal asymptote at y=0

E-mail Subject Line: Math 100 Your Name 10/8

1. Could a grasshopper ever be or ever have been the size of a dinosaur? Why or why not?
2. Evaluate 45/2 without a calculator.
3. Evaluate 8-2/3 without a calculator.

Reminders:

• I know you just had a midterm, but look through PS 4 and bring questions to class Friday.
• PS 4 is a group homework. You must turn it in with a group, not individually.

Due Monday 10/11 at 9am

Nothing! It's Fall Break!

Due Wednesday 10/13 at 9am

Review

• To read: Review Sections 2.2, 2.3, and 2.4.
• Be sure to understand: everything, of course!

E-mail Subject Line: Math 100 Your Name 10/13

Reminder:

• None!

Due Friday 10/15 at 9am

Section 2.5: Logarithmic Functions

• To read: pp 85-middle of page 89
• Be sure to understand: Why log(1) is 0; the two tables of values which roduce Figure 2.26--where did they come from? How are they related? ; Why logarithms grow so slowly; why logarithms have vertical asymptotes

E-mail Subject Line: Math 100 Your Name 10/15

1. What is log864?
2. What is log8(1/64)?
3. What is log8(square root of 8)?

Reminders:

• PS 5 is due Monday. Have done all the problems by Friday, and bring any lingering questions to put on the board during class Friday.

Due Monday 10/18 at 9am

Guide to Writing a Math Paper

• To read: all of it
• Be sure to understand: that writing a math paper isn't the same as writing a creative paper; that we usually don't build up the suspense by saving the solution until the end; that it's important to restate the problem, and to give a "game-plan" before stating the solution; that you do not need to use all the vocabulary you've learned in class to impress the person you're writing to.

Project 1

• To read: all of it
• Be sure to understand: the general scenario; what you are being asked to find

No questions today!

Reminder:

• Make sure you have passed gateways 1 and 2--more deadlines approach on Wednesday. Wednesday is the final deadline for Gateway 1, and the possible for Gateway 2 goes down some more.
• PS 5 is due Monday at 4pm, and is an individual assignment. Remember to e-mail Emily at ehowes if you have lingering questions on the problem set.

Due Wednesday 10/20 at 9am

Section 2.5: Logarithmic Functions

• To read: middle of p. 89-bottom of p. 91
• Be sure to understand: the log properties and identities

E-mail Subject Line: Math 100 Your Name 10/20

1. Use the log properties to simplify log8128.
2. Solve for t in the equation .5A0=A0(.87)t.

Reminder:

• Today is the deadline to receive 80% on Gateway 2 and any credit (50%) on Gateway 1, because:
• Gateway 3 is tomorrow. If you haven't signed up for it yet, make sure you do!

Due Friday 10/22 at 9am

Section 2.5: Logarithmic Functions

• Be sure to understand: the examples of pH adn Richter scales

E-mail Subject Line: Math 100 Your Name 10/22

1. Compare the intensity of an earthquake measuring 7.2 (like the one in Turkey) on the Richter scale with one measuring 4.3 (a mere tremor, usually can be slept through).
2. Compare the intensity of an earthquake measuring 7.7 (like the one in Taiwan) on the Richter scale with one measuring 7.2 (like the one in Turkey).

Reminders:

• PS 6 is due Monday. Have done all the problems by class on Friday and bring any questions with you to list on the board.

Due Monday 10/25 at 9am

Review:suggestions for reading a math text
Section 2.5

• Be sure to understand: The properties of the natural log are the same as the properties of log10(x); how to change bases for exonential and logarithmic functions.

E-mail Subject Line: Math 100 Your Name 10/25

1. Convert the function
P(t)=4.2(8.5)t
to an equivalent function having base e.
2. Convert the function
I(t)=4.2 log4(t)
to an equivalent function having base 8.

Reminder:

• Your project is due Friday. Get a rough draft ready, have all members of your group read it and make suggestions. Remember to follow the checklist (but don't write on it--it's for me to use when I'm grading your project). If you'd like to bring a rough draft in to me, please do!
• PS 6 is due today (Monday) at 4pm, and is a group assignment. If you have any questions, remember to e-mail Emily at ehowes before 4 on Sunday, to meet with her at 7 on Sunday night in SC 120.

Due Wednesday 10/27 at 9am

Section 2.6

• Be sure to understand: the table on pp 100-101. Scrutinize it! What's going on?

Section 2.7

• To read: pp 106-middle of p 109
• Be sure to understand: The relationship between a function and its inverse, algebraically and graphically.

E-mail Subject Line: Math 100 Your Name 10/27

1. Give a function which (eventually) grows faster than x5000.
2. Give a function which (eventually) grows slower than x.0001.
3. Consider the formulas given converting temperatures in degrees Celsius to degrees Fahrenheit, and vice versa.
• Convert 60oF to degrees Celsius.
• Convert your result back to degrees Fahrenheit.
4. Let f(x)=x3. It is a fact that f-1(x)=x1/3. Calculate
f-1(f(3)).

Reminder:

• Your project is due Friday. Make sure all members of your group are reading every draft and are making suggestions. Have a friend who's not in the class read your letter, and get feedback on whether they can follow it without reading the letter requesting your help.

Due Friday 10/29 at 9am

Section 2.7:

• To read: middle of p 109-113
• Be sure to understand: The two graphical methods for determining whether a function has an inverse.

E-mail Subject Line: Math 100 Your Name 10/29

1. Suppose the graph of a function is increasing and concave up. How would the graph of f-1 behave?

Reminders:

• Your project is due by 4pm Friday. Make sure you've all proofread it, make sure you've used spellcheck.
• PS 7 is due Monday. Have done all the problems, and bring questions on them to class Friday.

Here ends Chapter 2
Go to Chapter 4!

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 103
Norton, Massachusetts 02766-0930
TEL (508) 286-3970
FAX (508) 285-8278
jsklensk@wheatonma.edu

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