Interpret the periodicity of modeling functions

The  exercise appears under the Algebra II Math Mission. This exercise practices answering question about the context that concerns the periodicity of the graph, given the graph that models a real world context.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the graph that models the situation: This problem provides a word problem with real-world example of modeling functions being used. The student is asked to find the correct graph that matches the situation. Interpret the periodicity of modeling functions.PNG
 * 2) Answer the question about the word problem: This problem is similar to the first one, as it provides a word problem with real-world example of modeling functions being used. However, The student is expected to answer various questions about it from the multiple choice list or type a value in a text box.

Strategies
Knowledge of determining periodicity of modeling functions is essential for success while doing this exercise.
 * 1) All graphs that have the same wave-like shape, and that the maximum and minimum values are the same on each graph. What differs is the cycle length of each graph, or the period. If students can determine the period of the function from the context, then they can select the graph with the same period.

Real-life Applications

 * 1) Money as a function of time. One never has more than one amount of money at any time because they can always add everything to give one total amount. By understanding how their money changes over time, they can plan to spend their money sensibly. Businesses find it very useful to plot the graph of their money over time so that they can see when they are spending too much.
 * 2) Temperature as a function of various factors. Temperature is a very complicated function because it has so many inputs, including: the time of day, the season, the amount of clouds in the sky, the strength of the wind, and many more. But the important thing is that there is only one temperature output when they measure it in a specific place.
 * 3) Location as a function of time. One can never be in two places at the same time. If they were to plot the graphs of where two people are as a function of time, the place where the lines cross means that the two people meet each other at that time. This idea is used in logistics, an area of mathematics that tries to plan where people and items are for businesses.