Business4-math 108

Business4-math 108 - Math Learning Center Boise State 2010 Linear Modeling Business Mathematical Modeling is simply the act of building a

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Math Learning Center Boise State ©2010 Linear Modeling Business Mathematical Modeling is simply the act of building a model (usually in the form of graphs) which provides a “picture” of a situation that is based in a numerical situation. Linear Modeling is Mathematical Modeling where the graph is a line, hence linear. Linear Modeling occurs any time the rate of change is constant. Let’s build two examples. Example 1: An auto manufacturer has a factory which is open 24 hours a day and produces 10 finished cars per hour. This model has a constant rate of change in that each hour 10 additional cars are produced. Hence we will want to build a linear model. To begin to build our linear model, let’s pick two points How many cars will be built in an hour? ______ Enter the answer in point form: ( , ) (Answer in point form: ( 1 , 10 )) How many cars will be built in 24 hours? ______ Enter the answer in point form: ( , ) Now that we have two points, let’s create a graph. Wait, before we begin to graph, we must first choose letters to represent our variables. Since, we currently are in a math course, it would be easy to choose x and y as our representative letters. But what do x and y mean? Using the letters, x and y, in math makes perfect sense as we are able to move from one mathematical concept to the next with a strong level of consistency and thus, math is easier to learn from chapter to chapter and course to course. When we leave math and move to other subjects, such as business, we will choose letters which reflect the situation we are modeling. In this case, let’s use t to represent time in hours and n to represent the number of auto’s completed. In this case, a general point will be in the form ( t , n ). The variable t , representing time, is called the independent variable and will be placed on the horizontal axis when graphing. The variable n , representing number of autos completed, is called the dependent variable (this is because the number of autos completed depends on the time allowed). The vertical axis will be used to represent n . Side note: Many students have difficulty when we use letters other than x and y. When students enroll in other courses which use mathematical modeling and do not use x and y as the variable, they often have difficulty relating their other course to mathematics. In this
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This note was uploaded on 12/09/2011 for the course MATH 108 taught by Professor Alinaschimpf during the Fall '09 term at Boise State.

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Business4-math 108 - Math Learning Center Boise State 2010 Linear Modeling Business Mathematical Modeling is simply the act of building a

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