Blog Post 2
Maria Jose Garcia
1. Find a real world application OR
design your own experimental application relating to rates of change.
I
chose the recorded data of the population growth of a type of fish called
“walleye” on a pond in the course of 25 years.
2. Write a narrative or synopsis
explaining your application/experiment and include a question.
The
table below records the growth of walleye fish population throughout the
years. The information is recorded through a time lapse of 25 years. How fast
was the population growing at year 6?
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
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. Explain what you notice about the
ARC of these secant lines and what the calculations mean/represent in terms of
your experiment/application.
Points
Chosen: (6, 4476) (8, 4665) (10, 4786) (12, 4863) (14, 4912)
(4665-4476)/
(8-6) = 94. 5
(4786-4476)/
(10-6) = 77. 5
(4863-4476)/
(12-6)= 64. 5
(4912-4476)/
(14-6)= 54. 5
As
the points increase the slope goes decreasing representing how the population
of the walleye fish is decreasing as the years increase.
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.
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. Explain what
this calculation means mathematically and in terms of your
experiment/application.
My
tangent line goes through point x=6. The second point I chose was (10, 4950).
(Y2-y1)/
(x2-x1)
(4950-4476)/
(10-6)= 474/4= 118.5
The
IRC mathematically means the same as the slope of the tangent line. This
calculations will represent that there will be an approximate increase of about
118 walleye fishes per year at the pond.
8. Explain
in detail how you know that the value from part g is the IRC.
Since the calculations on part d are getting larger as the
years approach the point I chose, which was year number 6, I can notice the
value is getting closer to the tangent line, which would represent the IRC of the
population growth at year 6, but not exactly.
This post is neat and polished. You answered every point with a great math explanation that involves the topic that we are been introduced in class, limits. This experiment reflects how the instantaneous rate of change is applied to the population growth rate over time, which can be used as an excellent example to calculate limits applying the concept in the real life. I also like that your graphics are very precise.
ReplyDeleteGreat job. This post is very easy to follow. You chose data that is similar to mine. I choose to study the human population growth from the 20th century. Yours however has a bigger growth I am assuming because you started from Year 1 and I chose data after the population growth had stabilized.
ReplyDeleteI think I'm the only one in the group that didn't use population. I think you did a great job with your example. All of your graphs look great and very detailed. It definitely shows how you got the tangent line and the secant lines. The calculations were also really easy to follow
ReplyDeletemaria,
ReplyDeleteyou did a great job on this post. population growth is always a good way to analyze rates of change in real life. your graphs are very professional looking, as paula mentioned, as are your tables. i like that you used different colours to distinguish the tangent line on your final graph. additionally, your explanation of the IRC is spot on.
the only thing that you forgot to include were the units when calculating the secant lines. other than that, nice job!
professor little