MAT 212 – Week 5 Homework Hints

Most of the problems on this week’s homework came on problems involving instantaneous rate of change. There are two videos on instantaneous rate of change in the Chapter 11 Resources.

The first video covers the basic formula and the second applies these ideas to several applications like instantaneous velocity.

There are also a handout on finding the instantaneous rate of change of functions.

In these examples, the limit can be evaluated by doing some algebra. However, one of the problems on the homework involve the instantaneous rate of change of xlnx. This handout shows a similar problem where the limit is computed from a table of values.

Instantaneous rates of change are very important…if you have further questions, leave a comment.

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MAT 172 – Week 5 Homework Hints

Most of you did very well on this week’s homework. The only issues that came up were on the last two problems in the Section 2.5 Homework.

On number 6, you were given a system and asked to solve it with inverses. This is covered in the video below.

Ideally, you should use your graphing calculator or Excel to find the inverse since the row operations are ugly.

The last problem on the homework is similar to Example 4 in Section 2.5. The key is to attack part a first and write an equation for the total amount of copper. Then write two more equations for the total amount of zinc and glass respectively. Also make sure your variables are correct…try T = number of units of transistors, R = the number of units of resistors, and C = the number of units of computer chips.

If you have further questions, comment below.

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MAT 152 – Week 5 Homework Hints

Lots of things to look at this week from Section 2.3 and 2.4.

First let’s look at some of the problems from Section 2.3. You should have some experience with substitution and elimination from  Beginning Algebra and Intermediate Algebra. The videos I assigned you go over this topic extensively.

In addition, there is a narrated  example in the text on solving a system graphically where you have some fractions.

This problem is similar to the second problem on the homework.

In the application problems at the end, you are given several different types of problems. One type is the investing problem. The handout below works out a similar problem.

The other type of problem is the mixing problem.

These resources show how to set up and solve mixing problems.

In Section 2.4, three type of problems caused issues. For the basic on how to solve an inequality, the videos I assigned you give a good overview.

For most of you, solving the inequalities using a graph is new. Here is another video example from the textbook.

One of the application problems dealt with calculating grades. Here is a similar video example.

Another problem dealt with temperature…here is a similar video example.

I hope these resources are of some use to you. If you neeed to ask further questions on this homework, leave me a comment below.

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MAT 152 – Health Insurance Definitions

I have already had a number of questions about Project 2. If you have read the Project Letter (under the Projects button, Project 2 link in MyLabsPlus), you know this is all about comparing two health insurance plans. For many of you, these concepts are foreign since you may have never had health insurance or you may have been covered under your parent’s health insurance. Getting sick and not having health insurance is a quick road to severe financial difficulty. It is in your best interest to learn how it works so you can make good choices.

There are four key terms to understand: coinsurance, copay, deductible and out of pocket maximum.

Coinsurance – A form of medical cost sharing in a health insurance plan that requires an insured person to pay a stated percentage of medical expenses after the deductible amount, if any, was paid.

  • Once any deductible amount and coinsurance are paid, the insurer is responsible for the rest of the reimbursement for covered benefits up to allowed charges: the individual could also be responsible for any charges in excess of what the insurer determines to be “usual, customary and reasonable”.
  • Coinsurance rates may differ if services are received from an approved provider (i.e., a provider with whom the insurer has a contract or an agreement specifying payment levels and other contract requirements) or if received by providers not on the approved list. In addition to overall coinsurance rates, rates may also differ for different types of services.

 Copayment (copay) - A form of medical cost sharing in a health insurance plan that requires an insured person to pay a fixed dollar amount when a medical service is received. The insurer is responsible for the rest of the reimbursement.

  • There may be separate copayments for different services.
  • Some plans require that a deductible first be met for some specific services before a copayment applies.

 Deductible – A fixed dollar amount during the benefit period – usually a year – that an insured person pays before the insurer starts to make payments for covered medical services. Plans may have both per individual and family deductibles.

  • Some plans may have separate deductibles for specific services. For example, a plan may have a hospitalization deductible per admission.
  • Deductibles may differ if services are received from an approved provider or if received from providers not on the approved list.

Out of Pocket Maximum - The maximum dollar amount a group member is required to pay out of pocket during a year. Until this maximum is met, the plan and group member shares in the cost of covered expenses. After the maximum is reached, the insurance carrier pays all covered expenses, often up to a lifetime maximum.

  • Some plans, particularly Blue Cross Blue Shield, do not include the deductible in the out of pocket max. This is a marketing ploy since you will need to pay the deductible to reach the out of pocket maximum.

Another key concept to understand is the difference between a charge and a cost. When you go to a hospital, ER or any other type of medical service, the insurance company is charged some amount for the service provided. We will assume that this charge would be the same no matter what insurance plan you have. This is the amount an uninsured person would pay. However, an insured person may or may not pay that amount back to the insurance company for those charges. If your plan has a copay, you pay that amount instead…this is your cost. In short, a charge is what the provider charges the insurance company and the cost is what the insured actually pays for the service. As the charges increase, the cost to the insured goes up. In this project, you come up with a model of this relationship.

For most plans, the costs increases very quickly at first. This is because you must meet the dedeductible before the coinsurance kicks in. So if you have a $1000 charge for a trip to the ER before the deductible is met, you pay that entire amount. However, once you have paid the deductible by utilizing services, the charges are split between you and the insurance plan according to a set percentage given by the coinsurance. If your coinsurance is 40% and you have met the deductible, the $1000 charge costs you only $400. This applies until you reach the out of pocket max. Once you reach this preset level in costs, the plan covers all charges until the lifetime out of pocket maximum is reached.

In this project you will be comparing a plan you choose to the Basic Plus Plan. Assume that this plan is available to you. Also assume the charges for prescriptions and visits set out in the project letter. You will also complete this project as an individual. The space for Family in Tech 4 is there since in some semesters (not this one!) I have students to Family Plans.

I hope this helps you to understand the concepts and terms. If you have any further questions, leave me a comment below.

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MAT 212 – Typing Limits in Equation Editors

Since you need to prove your function is continuous, you have to find a way of typing a limit into your technical memo. It is pretty straightforward depending on whether you are using Mathtype or the equation editor in Word.

Equation Editor in Word – Open an equation box within Word by clicking on the Insert tab and then selecting Equation. Choose the button that says Limit and Log. In the first row you’ll see a limit template.

 

 

 

 

 

 

 Selecting this template will allow you to fill in the parts of your limit. You can find an arrow under the symbols.

 

 

 

 

 

 Mathtype – Once you have a Mathtype window open, select the Derivs tab in the bottom row of buttons.

 

 

 

On the far right you’ll see a limit button. Select this button and then modify the resulting equation to reflect the limit you want.

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Wired Magazine: The Man Who Could Unsnarl Manhattan Traffic

The article “The Man Who Could Unsnarl Manhattan Traffic” appeared in Wired magazine last Spring. At the time I thought it was very interesting considering that the person it describes, Charles Komanoff, did all of his work using Excel. And you all thought I was torturing you with learning Excel for nothing.

Komanoff has created a model for traffic and all of the different factors that impact traffic flow in Manhattan. And he did all of this with statistics and Excel! Excel is a standard business tool used in the real world. Learning the basic while taking this class should help you when you go looking for a job or when you take an accounting class.

Every graph you see in the handouts for your class is produced using Excel…I get some pretty impressive results. And a lot of you are getting very good at using Excel as well as Word too. Learning how to use these tools will pay off…if not in this class then perhaps in other classes.

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MAT 172: Writing Your Technical Memo for Project 1

You should now be thinking about writing the technical memo for Project 1. To help you, I posted a sample technical memo several weeks ago. Below you’ll find that memo with the feedback I left for the student who submitted it.

Before you start writing, make sure you reread the Project Letter. It is located under the Projects  button in MyLabsPlus. Select the link to Project1.

The paragraphs below describe some of the key parts of your memo in the context of Project 1. Let’s recap what you should have done so far.

  • Technology Assignment 1 – You found the equations for the amount of water to be pumped from the three wells.
  • Technology Assignment 2 – You put the augmented matrix for your system in reduced row echelon form.
  • Technology Assignment 3 – You used Excel to verify your work from Tech 2

The last thing you’ll need to do before writing is to find the solutions to your system using the reduced row echelon form. All of this needs to be organized in your technical memo. Your audience has about the same background in math that you do, but it may have been a while since they took Finite Math.

Introduction – In this section, you introduce the problem you are solving along with the data you will be using. This means you’ll need to give all of the data that has been supplied to you to establish the starting point of your analysis. Make sure you also indicate exactly what it is you will prove.

Methods – This is a section where you will explain what your strategy is. You do not work out your calculation here…instead, you need to explain the background. What information will you use to write out your equations? What are your variables and what do they represent? You may choose to explain what your equations are in this section or in the Results section. You’ll also need to explain how the process for solving the equations works…augmented matrix, row operations, ect.

Results – In this section you’ll work throught the strategy explained in Methods. Using complete sentences, present and solve you equations.

Discussion – Having the solution is just a part of the process. You also have to know what it means. There should be many solutions to your system of equations. However, not all of them may meet the requirements of the problem. In this section, you’ll want to screen your solutions and pick out the ones you’ll recomend the City of Bad Water use. If there are no solutions that work, can you make a recommendation to the city that might allow them to meet their requirements?

If you have any questions about these parts, leave your question in a comment below.

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MAT 212: What Should Be In The Technical Memo for Project 1?

A few weeks ago I posted a technical memo for a project in College Algebra. I wanted to give you an idea of what a technical memo looks like. In addition, you’ll find information on the parts of the memo in the link “How Do You Document Your Solution?” under the Projects button in MyLabsPlus. Below is the sample technical memo with the comments I left for the student who wrote it.

Many of you are getting started on writing your own memos for Project 1. Before you start writing, make sure you reread the Project Letter. It is located under the Projects  button in MyLabsPlus. Select the link to Project1.

The paragraphs below describe some of the key parts of your memo in the context of Project 1. Let’s recap what you should have done so far.

  • Technology Assignment 1 – You found a health insurance plan and created a table of charges and total cost.
  • Technology Assignment 2 – You  put the table into Excel and used it to make a graph of total cost as a function of the charges.
  • Technology Assignment 3 – You found the piecewise linear function for the graph and pasted it into a Word document with the graph.

The last thing you’ll need to do before writing is to prove that the function you have found is a continuous function (Section 11.2).

All of this needs to be organized in your technical memo.

Introduction – In this section, you introduce the problem you are solving along with the data you will be using. Assume the person reading your technical memo has the same general knowledge that you did at the beginning of this project. You’ll need a table of all of the critical information that you need to create your table. Make sure you also indicate exactly what it is you will prove.

Methods – This is a section where you will explain what your strategy is. You do not work out your calculation here…instead, you need to explain the background. Define the important terms like copay, deductible, coinsurance, and out of pocket maximum. Explain the relationships between the different columns in your table. How are costs calculated before the deductible is met, after it is met but before the out of pocket max is reached, and after the out of pocket max is reached. How do you find the piecewise linear function from the table?Another term to define is continuity at a point…since you’ll need to prove that your functions is continuous, you’ll want to supply a definition of that term.

Results – In this section you’ll work throught the strategy explained in Methods. Using complete sentences, present a table of charges and total cost. This does not have to be identical to the ones you did in the tech assignments, but should contain the information needed to get the piecewise function. Then show the graph and the calculation for finding the piecewise linear function. Finally, you’ll need to calculate some limits to prove that your function is continous.

Discussion – This is where you discuss the significance of your results. Is there anything anything you noticed about your function? How does this relate back to your plan? Is it good for a plan model to be continuous? Why?

If you have any questions about these parts, leave your question in a comment below.

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MAT 152: Week 4 Homework Hints

Two types of problems caused consternation on the Week 4 Homework.

In the homework from section 2.1, the last two problems led to some incorrect answer. In these problems, you must put a value into the given line and solve for the other variable. One possible issue is putting the value in for the wrong variable…the other is putting the wrong value in due to the fact that the variable has been scaled. The way to avoid these pitfalls is to carefully write out what each variable represents…like I do in these handouts

Make sure your description include what the variable represents as well as the units (like thousands of dollars).

The other issues came in section 2.2 where you needed to put in data and find a line via linear regression. Some of the problems may be due to lack of training in using the calculator…here are the handouts on doing linear regression on the calculator and in Excel.

Now wait you say…I followed these handout religiously and was getting crazy stuff! So far, every student saying this failied to ALIGN the data when they entered it. In other words, it wasn’t the calculator. For instance, one of the problems contained a data table like the one below.

Year Population (millions) Year Population (millions)
2000 275.3 2060 432.0
2010 299.9 2070 463.6
2020 324.9 2080 497.8
2030 351.1 2090 533.6
2040 377.4 2100 571.0
2050 403.7    

In this problem, the data for the years is supposed to be entered as “years since 2000″. This means that when you put the numbers into L1, you put them in as below.

Years since 2000 Population (millions) Years since 2000 Population (millions)
0 275.3 60 432.0
10 299.9 70 463.6
20 324.9 80 497.8
30 351.1 90 533.6
40 377.4 100 571.0
2050 403.7    

Make sure you scale your windows according to the aligned data and not the original data…I think this will fix the problems many of you have been having.

If you have further questions, comments below.

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MAT 152: What Should Be In Your Technical Memo for Project 1?

I posted a sample technical memo in a earlier post. You might be curious with about the comments I gave to the student that submitted that technical memo.

 As for the technical memo that you are working on right now, it will need to have 4 sections: the Introduction, Methods, Results and Discussion. Using this document, you will explain how you calculated the savings between attending two year college for 2 years and then four year college for the last two years, versus attending four year college for four years. In the technical memo you explain the strategy for doing this and also carry out the strategy.

Introduction – In this section, you introduce the problem you are solving and the data you will use to solve the problem. Assume your audience is unfamiliar with the particular problem you are doing, so you need to explain what state you are researching as well as the types of colleges you will analyze. At the end of the Introduction, make sure you answer the basic question about difference in cost. By doing all of this in the Introduction, you are laying out the starting point and the ending point for your analysis.

Methods – In this section, you describe the strategy you followed to go from the data to the final solution. This is not where you carry out the calculation…the exception is if you do the same calculation several times. Then you can do a sample calculation to illustrate the process.

You’ll need to explain what was graphed in your scatter plot, what points you used to find your line, and the mathematical tools you used to find the lines. It is a good idea to use function notation and name your lines…it will make it easier to refer to the lines. Explain how to use the functions to find the cost savings between 2/4 year college attendance and 4 year college attendance.

Results – This is where the fun begins. In this section, carry out the strategy you described in Methods…do the calculations. You’ll need to use sentences (like in Tech 3) to help your reader follow your work. 

Discussion – This is often a tough section to write…In addition to stating the main result, you need to talk about any factor that might change this result. For instance, how would using a different set of point change the answer. Why were the points you used a better choice than other pairs of points? You can also end your Results with the two lines, and then carry out the comparison of lines and the calculation of the difference in cost in the Discussion. Other possibilities are OK too.

If you have any questions about the format of the technical memo, comment below.

Posted in College Algebra | 2 Comments