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Mathematics are used to model situations. Information is collected and mathematical models are created to represent the activity. 

Example: A tech support firm charges a flat fee in addition to a certain cost per hour. For one job that took two hours the firm charged $250. For a five hour job they charged $550. How much is the initial cost, and how much is the per-hour fee?

Let’s consider x to be the number of hours, and y is the cost.

It is possible to find an equation that fits the two points.

First, using the formula for slope, we have:

Next, using the point-slop form of the equation, we find the slope-intercept form.

(y – y₁) = m(x – x₁)
(y – 250) = 100(x – 2)
y – 250 = 100x – 200
y = 100x + 50

Now, the meaning behind this equation:

The 50 represents the initial fee. The 100x represents the charge per x hours. The initial fee is $50 and the company charges $100 per hour.

Using this equation, we can predict what the cost of a job that requires seven and a half hours of work.

y = 100(7.5) + 50 = 750 + 50 = 800

For seven and half hours of work, the cost would be $800.

From here, we can write this equation as function. The cost of the job is determined by the function f(x) where x represents the number of hours the jobs take.

f(x) = 100x + 50

RESEARCH PROJECT

For this class, pick a situation that relates two variables or factors that have some sort of association.

Examples:

• Temperature and stock market prices
• Unemployment and crime rates
• Precipitation and TV ratings

Find three pairs of data, with each pair having a value associated with one of the factors. Using two of the pairs, find a function that describes the relationship. With the third pair, test the function.

You will be required to:

1. Find three pairs of data
2. Form an equation using two pairs
3. Evaluated accuracy of equation to the third pair of data
4. Create a graph with the three pairs and the appropriate line.

The final paper should be in APA format.

The project consists the following assignments:

1. Build-A-Function – Topic
2. Build-A-Function – Points
3. Build-A-Function – The Function
4. Build-A-Function – Graph
5. Build-A-Function – Completed Project