Adrian Simion Blog Post 2

Adrian Simion Blog Post 2:

Part a: 

      a.     Find a real world application OR design your own experimental application relating to rates of change.

          My real world application relating to rates of change is through the analyzation of the greatest player to have ever played the game of basketball, LeBron James. I will be calculating the rate of change for his games played from his 12 seasons in the National Basketball Association. 

     

      b.     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 data set I chose shows the relationship between the season LeBron participated in and the amount of games per season that he played in regular games. Therefore, the question I will ask my fellow readers; During his 6th Season as an NBA player what was LeBron James rate of change for games played?   

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

      

       

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

      

      e.     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.

       The three points I have selected are:

        Point: (4,78)                    1.) (5,75)                2.) (6,81)                  3.) (7,76)

       

                                      (75-78)/(5-4) : -3               (81-78)/(6-4):  1.5              (76-78)/(7-4):  -2/3

          The slope tends to fluctuate and are not at all linear. This shows that in the LeBron James tends to fluctuate his games played every season. The higher his games played, the better because that means he played in many more games having the ability to win more games. The slopes show that his games played from his first year to the second year current one doesn't fluctuate that drastically but has a slight increase when graphed. However, from his second year to his fifth year, he decreases the amount of games played resulting in his performance from previous years to also decrease because of the lack of games that he has played.

      f.      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)

        

      

      g.     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.

          (4,78)        Point Q: (8,79)           (79-78)/(8-4):  1/4=   {. 25}

    

          This means that at this particular point in time LeBron James' games played had a slight increase by .25 from his 4th year to his 8th year

  

      h.     Explain in detail how you know that the value from part g is the IRC. 

      

     It was important to narrow in the results because we wanted to find out the value to determine the direction in which Lebron James' games per season was either increasing or decreasing.  For the value selected, the slope was actually slightly positive, which showed us that his games per season would slight increasing every season before his injury in season 9. After season 9 his games per season again began to slowly increase. The values are slowly starting to get closer to the tangent line which would then represent the IRC for LeBron James' games per season.