Model situations by combining functions using arithmetic operations

The  exercise appears under the Algebra II Math Mission This exercise practices combining functions using the appropriate arithmetic operation in order to model a more complex situation, given two basic modeling functions.

Types of Problems
There is one type of problem in this exercise:


 * 1) Write the formulas: This problem provides a real-life examples of functions being used, and students are asked to write two different formulas for ___ in terms of ___. Model situations by combining functions using arithmetic operations.PNG

Strategies
Knowledge of combining functions would help to ensure success on this exercise.
 * 1) A formula for $$I(t)$$ in terms of $$C(t)$$ and $$P(t)$$ is $$I(t)=C(t)\times P(t)$$
 * 2) Accuracy can be increased by writing down the values on scratch paper before submitting the answer.

Real-life Applications

 * 1) The problems of this exercise can be viewed as real-life applications.
 * 2) 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.
 * 3) 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.
 * 4) 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.