Blog post 2

Carlos Torres Delpin Blog Post #2
February 10, 2015

Part A:

1. Find a real world application OR design your own experimental application relating to rates of change. (in the blog folder you will find plenty of examples to get you started).
The real world example I chose to investigate for this blog post was the ERA of Roger Clemens from 1985 to 1995. 

2.  Write a narrative or synopsis explaining your application/experiment and include a question. (for example, what is the velocity of the snowball at exactly 2 seconds? Or how can I find the velocity of the baseball at exactly 3 seconds?)
The table provided below demonstrates Clemens' ERA from 1985 to 1995. The numbers 1-11 represent the years 1985 through 1995. With this information I will be able to know what the instantaneous rate of change for Roger Clemens ERA is on any given time. What do you think the instantaneous  ROC will be in the year 1985?  

3.  Create a table of values for the data that you have recorded from your application/experiment.

4.  Graph the points using the data from your table of values (connect the dots). 

5.  Calculate the slope (ARC) of at least three secant lines originating from the same point on your graph to three different points on your graph (i.e. maybe you want to know what happens exactly at x = 20, so your points might be (20, 62), (20, 56), (20, 50)).  Explain what you notice about the ARC of these secant lines and what the calculations mean/represent in terms of your experiment/application.

Since I wanted to find out the instantaneous ROC in the year 1985, I will see the ROC's between 1986, 1987, 1988. 

From t=1 to t=2:

(2.48-3.29)/(2-1) = -0.81

From t=1 to t=3:

(2.97-3.29)/(3-1) = -.405

From t=1 to t=4:

(2.93-3.29)/4-1= -0.12

I    In baseball, the ERA is not measured as a linear graph, due to the fact that every year the amount of earned runs permitted by pitchers varies. A negative slope represents an improvement in the pitcher's ERA while a positive slope represents an worsening of the pitcher's overall performance. 

     

   6.  Sketch an approximation of a tangent line that passes though the same point (P) from part e to which you connected your secant lines (i.e. you would draw a tangent line through the point 20, since that is the same point that you used to calculate your three different secant lines)

      

   

   7.  Choose a second point (Q) on the tangent line, and calculate the slope of the line (PQ). This calculation will be the instantaneous rate of change ((IRC or derivative at a point)…be sure to identify the units correctly).  Explain what this calculation means mathematically and in terms of your experiment/application. 

    I used the points (1, 3.29) and (2.5, 2.48) from the tangent line. The result I got was -0.54. This means that from t=1 to t=2 the instantaneous ROC was -0.54, meaning that his ERA was going down. 

   8. Explain in detail how you know that the value from part g is the IRC. (i.e. since the values of calculations from part d are getting smaller and smaller, this shows that the slope of the secant is getting closer and closer to the tangent line … or some explanation similar to this). BE DETAILED!!!

    The value from part g is the IRC because it indicates that at a certain moment between t=1 and t=2, values began to get smaller and smaller until they reached their limit, which was -0.54. This means that Roger Clemens' ERA was improving through this time period.