a.
Find
a real world application OR design your own experimental application relating
to rates of change. (
--How the
population of Walleye will act within 25 years
b.
Write
a narrative or synopsis explaining your application/experiment and include a
question.
c.
Over
time the fish will reproduce amoung themselves, How many fish will be breed on
the 26th --year
d.
Create
a table of values for the data that you have recorded from your
application/experiment.
Started
from 10-25 on graph
Y2-y1/x2-x1 y2- (4786)/x2-(10)
4829-4786/11-10=43/1=43
4836-4786/12-10=50/2=25
4890-4786/13-10=112/3=37.3
^^^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.
----
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)
--- refer to graph above , blue line
e.
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.
------ 4300-4218/7-6 82/1
the jump from one year to another is 82 units of fish per year
f.
Explain in detail how you know that the value
from part g is the IRC. DETAILED!!!
While
the part d calculations are clearly going up it shows that the slope of the
secant is getting further from the tangent line
Great job on the graph! Its really good that you showed all the calculations so clearly. The example you used is a good one for this assignment
ReplyDeleteGood work and I like the graph. Good stuff.
ReplyDeleteNice job. Grape is a little confusing but you do a great job explaining how to use the secant line and determine that growth of the specified point.
ReplyDeleteI just commented on one of your classmates who used the same data! Like I commented on hers, I have similar data to yours. Mine was about human population growth in the 20th century: after the population growth had stabilized. Perhaps next time, I would include a break in the y intervals on the side so that your have a better window to display your data points on the graph.
ReplyDeleteThe first graph looks great. I can't see the second graph though. But I like the example you used and the explanation is clear and concise so I'm not really missing the graph haha
ReplyDeleteI had the same experiment and got very similar data to yours and results! Good job!
ReplyDeletemarek,
ReplyDeleteyour experiment is good. your tables and graphs are organized well, although it was hard to see the second graph, which i am guessing has the tangent line that you drew. (i like that you drew them on a chalkboard!) your initial question, however, does not match the rest of your experiment. if you wanted to discover what is happening at t = 10 years, your question should have been worded as "in year 10, how fast is the population growing?" the only other thing missing from your post is to include units with your tangent and secant calculations.
other than a few bumps, good job. =]
professor little