A) Find a real world application or design your own
experimental application relating to rates of change:
A pond was stocked with a type of fish call “walleye” and
over a 25-year period, the population of the fish has increased. Initially, the population of the fish was
3000.
B) Write a
narrative or synopsis explaining your application/experiment and include a
question:
What happens to the to the population of fish at exactly
5 years?
C)
|
Year
|
Walleye Population
|
|
0
|
3000
|
|
1
|
3400
|
|
2
|
3720
|
|
3
|
3976
|
|
4
|
4181
|
|
5
|
4345
|
|
6
|
4476
|
|
7
|
4581
|
|
8
|
4665
|
|
9
|
4732
|
|
10
|
4786
|
|
11
|
4829
|
|
12
|
4863
|
|
13
|
4890
|
|
14
|
4912
|
|
15
|
4930
|
|
16
|
4944
|
|
17
|
4955
|
|
18
|
4964
|
|
19
|
4971
|
|
20
|
4977
|
|
21
|
4982
|
|
22
|
4986
|
|
23
|
4989
|
|
24
|
4991
|
|
25
|
4993
|
E) find the
population at exactly x=5 (5,4345). I
will draw three secant lines with the points: (3,3976), (4,4181), (6,4476),
(7,4581), (8,4665)
-
y2-y1/x2-x1= 4345-3976/5-3= 184.5
-
y2-y1/x2-x1= 4345-4181/5-4 = 164
-
y2-y1/x2-x1= 4476-4345/6-5 = 131
-
y2-y1/x2-x1= 4581-4345/7-5 = 118
-
y2-y1/x2-x1= 4665-4345/8-5= 106.67
the thing I
am noticing about the rate of change of the secant lines is that the rate of
change is decreasing as we move towards year 5 and away from year 5. Also, the difference between the rates of
change fluctuates. However, since the
difference in population is less as the number of years increases then the rate
of change will continue to decrease.
G) (7,4600)
IRC=
y2-y1/x2-x1= 4600-4343/7-5= 128.5
This means
that at exactly point 5, the rate of change is 128.5
H) According
to part d of the experiment, the population is beginning to increase at a
slower rate as the number of years is growing.
The IRC proves that the population of the fish is increasing per/year
but the population change is according to the year itself. And in year 5, the population has increased
I liked the experiment that you chose because it made me research more about that fish, hope its population keeps growing. Also enjoyed your graph, very detailed!
ReplyDeleteGood job! I chose the same experiment and got similar results to these ones. Your graph is neatly drawn and detailed for the readers to understand. I liked it very much!
ReplyDeletegeorge,
ReplyDeletepopulation growth is always an accessible topic for discussing rates of change, so good selection. i like how you chose values on both sides of t = 5 years so as to better see the zooming in effect of the IRC.
your explanation of your results could have been a little more detailed by saying something like the population is increasing at a rate of 128.5 fish per year. also, remember to include your units for each secant calculation because those number mean something.
overall, good job, though. =]
professor little