Research Project - Build-A-Function
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:
|
m
|
=
|
y2 - y1
---------
|
=
|
550 - 250
------------
|
=
|
300
-----
|
=
|
100
|
|
x2 - x1
|
5 - 2
|
3
|
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
- Precipitationand 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.