Learning Resources
Lesson
During this part of the chapter, you will be given the opportunity to use the mathematical concepts that you have learned. The Case Study problem will reflect the general nature of the chapter. This problem requires you to use the key skills, knowledge, principles, processes and concepts presented in this unit. You will be able to challenge these problems and may be requested to do part or all of the work. Consult your teacher.
The Extension section may require an extension of the material covered in the unit and will provide a strong challenge for you. These problems may involve applying procedures to situations that are similar to those in the chapter but unfamiliar or altering procedures to deal with new situations. You may need help to complete these.
- Case Study 1 Drawing Pictures
- Case Study 2 Shaking Hands
- Extension Annuities
Case Study 1: Drawing Pictures
In this project you will have
- to graph functions of various types on TI-83 or some other graphing technology
- adjust the windows on the graphing calculator to successfully graph all functions
- work with, and account for, restrictions on the variables in a function.
To graph the function 
with the restricted domain 
, click here for a viewlet describing the procedure on a TI-83. Note to enter the restricted domain on the TI-83 it has to be written as two separate inequalities : 
.
For question 1, the five functions should be graphed together on the same plane. To determine the proper window look at the range of values for all domains (x) values and select an Xmin and Xmax that will include all the values. From these determine your Ymin and Ymax .
For question 2, a picture is given and you have to develop equations with proper restrictions to graph it. The water level can be modeled using a simple linear equation for a horizontal line. A hint for the two curves would be to think about logarithmic and exponential functions.
Case Study 2: Shaking Hands
In this project you will have
- organize and collect data
- fit a curve to the data once it is plotted on a scatter plot
- realize what type of curve is being represented by the data and find an appropriate equation
- apply your understanding of exponential functions to real life situations to solve a problem
To complete this simulation, obtain a copy of Blackline Master 3.PIT.1 from the Teacher Resource Book from your in-school teacher. If you are in a small class, attempt to get data for at least five handshakes completed.
This simulation is meant to model the spread of a virus, such as the flu or cold virus. One student will represent the original carrier of the virus and the gloved handshake will not pass on the virus and the ungloved handshake will. Therefore, the fourth column in the Blackline Master will represent the number of infected people after each handshake is completed.
Any further clarification can be obtained from your on-line teacher.
Extension: Annuities
Annuities is a topic that is of interest since it an apply to savings as well as mortgages. One of the largest purchases that you will ever make is a home and as such a mortgage to repay the loan. It becomes very surprising to many people that after half the mortgage payments on a 25-year mortgage are paid more than half the principal still remains. Amortization tables is an interesting idea to explore even though it is not done in this extension.
Read and study the given material and answer the questions.
Activity
Complete case study and extension as directed by your teacher.
Test Yourself
There is no self test for this lesson.