Miles Blog 2, Really good work, A+

Instantaneous results!

Blog submission number 2

Due Date: February 9, 2015 by 11:59 pm Eastern Standard Time

Point value: (20 points)

Directions:

(When creating your problem, be sure to take note of these directions as well as the criteria in the rubric) here is a worked example of what you will do on your own using the instructions below.

Part a:

a.     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)

A population of walleye over 10 years after it being introduced .

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?)

What is the rate of growth of the population after 5 years of it being introduced?

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.

(4181-3976)/4-3= 205

(4181-3720)/4-2= 230.5

(4181-3400)/4-1= 260.333

The ARC is decreasing as the number of years go on.

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.

4400, 5.25

(4181- 4400)/4-5.25= 175.2

The number of fish is increasing at approximately 175.2 per year.

h.     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!!!

Since the values are getting larger and larger but the ARC is decreasing (from part D), 175.2 shows a more average IRC. The slope of the secant is getting closer to the tangent line.