Welcome.

Here you will see info about what we did in class, upcoming exams, solutions for past exams, etc.,

SYLLABUS

CHECK AT LEAST ONCE A WEEK!!

Started 1/14/2016

Updated 4/29/2016.

Grades have been posted on Bisonweb.

BRIEF SOLUTIONS FOR FINAL EXAM

STUDY ALL MATERIAL FROM THIS PAGE

HW20 (DUE NOON MON 4/25): Download this Excel chart showing dc temperatures from 1995 to 2012 and email it to me after doing the following:

1) Calculate average annual temperature for each year and enter in row 16. I have done it for 1995. If you click on it you will see formula I used. Do the same for all the years. (Actually this can be done in one shot using "fill right" function from drop down menu under "edit" after highlighting the empty cells to the right of the one that I have filled).

2) Draw a chart showing average annual temperatures, average winter temperatures, etc., from 1995 to 2012 on same graph, also on the same excel sheet.

video on using Excel to make charts

GO HERE FOR THE WIKIPEDIA ASSIGNMENT

Updated 4/21/2016.

SOLUTIONS FOR TEST III

For test3 study all homework problems from hw14 onwards. More details to follow.

Updated 4/14/2016

HW18 is open WEBWORK and it closes monday night at 10pm.

More details and hints on HW below the announcements

IMPORTANT ANNOUNCEMENTS: There is no class tomorrow (friday). i will be in office 10 to 1 if you have questions on hw or other things. Also note the information about the upcoming test 3 on wednesday on update page. HW 20 will be announced soon. IF YOU ARE GRADUATING OR NEED TO IMPROVE GRADE PLEASE GET STARTED ON EXTRA CREDIT ASSIGNMENT ON WIKIPEDIA RIGHT AWAY. THIS IS NOT SOMETHING YOU CAN DO AT LAST MINUTE. SEE PREVIOUS EMAIL FOR DETAILS.

HW19 is also easy, and based on the statistics handout on the update page as well as class notes from yesterday. If you were not in class wednesday please talk to someone who was.

The only thing that you might need to know in addition is how to find the mean and variance when a probability table is given (problems 4 and 5). This is similar to how you do it from a frequency table as shown in class. Only difference is that probability P(x) plays the role of relative frequency, so you don't need to divide by the total number n at the end, because that is built into the relative frequency (here probability). So you add the products x times P(x) for all the values of x to find the mean mu. Once you know the mean mu you find variance by adding (x-mu)^2 times P(x) for all the values of x. Then standard deviation is just the square root of variance.

For problem 1 note that you are finding the SAMPLE MEAN, etc in this case because you have a sample, not the whole data set, and you are dividing by n-1, not n (total number of values).

Updated 4/12/2016

HW18 is online on WEBWORK

It closes thursday night at 10pm.

It is also easy, and based on the statistics handout on the update page as well as class notes from yesterday. If you were not in class today please talk to someone who was. The only thing that you might need to know in addition: Q3 means third quartile. It is the value in the data set such that only 25% of the values are above it.

Updated 4/8/2016

We will use material from the following for the material on statistics both in class and in the homeworks.

Updated 4/6/2016

We will discuss this in class today.

All you need to know for this homework:

Probability of an event = Number of favorable outcomes divided by total number of outcomes.

Please note that I won't be available by email after 3pm on friday.

Updated 4/1/2016

Comments that will help with HW15

If you have questions you can ask in class on monday.

Updated 3/29/2016

Comments that will help with HW14

More helpful videos on probability:

Probability that at least 2 people in a room of 30 have same birthday

Binomial probability formula

If you have questions you can ask in class on wednesday.

Updated 3/25/2016.

SOLUTIONS FOR TEST II

We went over hw13 in class today (3/23).

TEST II BASED ON PROBLEMS FROM HW7 ONWARDS.

SUMS OF ARITHMETIC AND GEOMETRIC SEQUENCES, PROBLEMS ON FINANCE, PERMUTATIONS, COMBINATIONS AND BASIC PROBABILITY.

REVIEW IN CLASS ON WED, 2/23

Updated 3/14/2016

Due Monday 3/21 by 9.59 pm online on WEBWORK

Comments that will help with HW12

More helpful videos on permutations and combinations:

factorial-and-counting-seat-arrangements

combinations-number of handshakes

combinations-number of 9 card hands

If you have questions you can ask in class on monday. On monday I will discuss formula 3 (see hw12 comments above) and also go over some of the problems.

Updated 3/9/2016

You only need to know the permutation formula nPk for arranging n different things in k places and that if repetition is allowed there are n^k ways to arrange n things in k places.

The idea behind both of these formulae is that you just multiply together the number of ways you can fill each place.

See the following videos if you didn't come to class this week:

permutation-formula

possible-three-letter-words

If you have questions you can ask me on friday.

Updated 3/5/2016

Comments that will help with HW10

If you have questions you can ask in class on monday. On monday we will start with combinatorics (how many ways an event can happen ? ).

Updated 3/1/2016

Comments that will help with HW9

If you have questions you can ask in class on wednesday.

Updated 2/26/2016

Comments that will help with HW8

If you have questions you can ask in class on monday. On monday we will go over sums of infinite geometric sequences.

Login instructions below.

Updated 2/23/2016

Comments that will help with HW7

You also need to come to class in order to do this hw because we will go over much of the material used in it. Right now we have gone over sums of arithmetic sequences. On wednesday we will go over sums of geometric sequences.

Talk to me during office hours wednesday or thursday if you need more help

Login instructions below.

Updated 2/20/2016.

SOLUTIONS FOR TEST I

Updated 2/14/2016

Comments that will help with HW6

Talk to me during office hours wednesday or thursday if you need more help

Login instructions below.

Updated 2/11/2016

Video related to hw5. Details on hw5 below.

Video about half-life and doubling time (More where they come from! :-) )

This video also explains how half-life and doubling time formulae end up being the same, even though the exponent is negative in exponential decay equation.

LINEAR, QUADRATIC, EXPONENTIAL FUNCTIONS AND TOPICS ON SEQUENCES COVERED BY FRI, FEB 12

BASED ON HW PROBLEMS GIVEN UNTIL WED, 2/17

REVIEW IN CLASS ON WED, 2/17

Updated 2/9/2016

I will answer questions on this in class tomorrow.

Comments:

The main formula you will need is k = ln2/T where T is doubling time or half life. (If you replace ln2 by ln3 you will get tripling time, and so on).

Problems 1: keep everything in hours or everything in minutes. Use the formula above to find k using the half-life given. Put this k into the equation given. Now just plug in the time t to get the answers.

Problem 2: (a) solve for k using logarithms.

(b)percentage growth rate is given by (N(t+1)-N(t))/N(t) times 100.

(c) Use formula above to find T, doubling time. Round to 4 decimal places.

Problem 3, part 2: same method as Problem 2(c).

Problem 4 might be the most tricky, but you can do it using what we know. Let t be the unknown and solve for it using logarithms. You will need to simplify first using properties of exponential functions (such as a^t/b^t = (a/b)^t).

Problem 5: straightforward, if you got the first 4.

For help with definitions etc., see class notes or "Basics of Exponential Functions" below.

Talk to me during office hours thursday if you need more help

Login instructions below.

Updated 2/5/2016

Comments:

Problems 1,2 and 3 are straightforward.

For problem 4 assume that it grows according to the natural exponential function. So your formula will look like the continuous growth (or continuous compounding interest) formula P(t) = P(0)e^(rt).

Problem 5 the first 3 parts are easy. For part (d) you will solve for t as usual using logarithms except that here the base b is not equal to e. So instead of the power being equal to ln(*) it will equal ln(*) divided by ln(b). In other words, you need to use change of base formula.

For example if you had 2000 = 1000(1.1)^t then canceling off 1000 you get 2 = 1.1^t, and then to solve for t you will divide ln(2) by ln(1.1).

For help with definitions etc., see class notes or "Basics of Exponential Functions" below.

Talk to me during office hours monday if you need help

Login instructions below.

Updated 2/1/2016

Tutorial on Geometric Sequences (ignore the part on "Sums" for now)

Basics of Exponential Functions

Comments:

Problems 1 and 2 are straightforward. For problem 5 use tutorial above.

You can do problem 3 using compound interest formula discussed in class.

For part (c) the number of years t you put in the formula you got for part (a) will be negative if the year is before the starting year.

For example if in (a) it is 2003 and in (c) it is 2000, put t = -3 in part (c).

For problem 4 see class notes. Also look at "Form 1" and "Form 2" in the "Basics of Exponential Functions" above.

Talk to me during office hours wed and thu if you need help

Login instructions below.

Updated 1/26/2016

Login with username first initial last name (example: Barack Obama will be bobama) and password the

You can also practice by logging in as practice1 or practice2 etc., Password is also practice1, practice2...

Video (a bit messy -- sorry!) Tutorial about webwork and the first homework

You will need to login to blackboard to see this.

Useful tutorial (from West Texas University) about quadratic functions and graphs. We will NOT use vertex form, instead use the formula x = -b/2a to find the x-coordinate of the vertex.

Updated 1/14/2016

Here are the prices of solar panels over the years:

The first number (to be on x-axis) is the year and the second number (to be on y-axis) is the price per Watt in 2012 dollars:(approximately)

(1980, 24), (1990, 8), (2000, 4), (2010, 2).

1. Using the video (below) if necessary, enter this data into an Excel spreadsheet and graph them with the years on the x-axis and prices on y-axis. is the graph a straight line?

2. Check by finding the slope between different points. If it is a straight line, then the slopes will be the same no matter which two points you choose.

3. Do the numbers 24, 8, 4, 2 form an arithmetic sequence? If yes, give the formula for the n-th term.

4. Same question as (3) for 12, 8, 4,...What would be the next term? What would be the n-th term?

LEARNING MATERIAL:

video on using Excel to make charts

Tutorial on finding slope of a line from two points

This page has other videos on the equation and graph of a straight line.

Tutorial on arithmetic sequences

For now study only the first part where they talk about how to find the formula for the n-th term. We will do the summation part later.

They use the symbol x_n instead of s_n for the n-th term and it is a better notation because s_n is usually reserved for the sum of the first n terms.