Test Two Study Guide - Spring 2014 - Tuesday, April 22nd
Constrained Growth population model. An island of rabbits that has a specfic carrying capacity. S-shaped growth instead of exponential growth.
Growth Rate equation is:
Growth Rate = Growth Rate Constant * (1 - Population/Carrying Capacity)
or Population
Growth Rate Constant * (1 - -------------------)
Carrying Capacity
Understand the effect of adding
a carrying capacity and how the above
equation changes the simpler population model
from EXPONENTIAL GROWTH
to growth graphed by an S-shaped curve.
(See Fig. 1.3. Six shapes to represent dynamic patterns...)
See especially #1 and #2 and #11
for the NetLOGO Game of LIFE model
concepts and
sample practice questions from previous tests.
See especially #3 on Monte Carlo throwing darts
to estimate the AREA of a region:
i.
ii.
iii. b
iv. a = ----- d
v. c
vi.
b
Do you understand the a = --- (d) formula and concepts.
c
Can you look at a Monte Carlo problem
and find the a,
the b, b
the c, The -----
the d? c
and figure out which of the four parts is the goal, the unknown?
It is all in the above study guide PDF. See page CCC. See CCC.
BICTION = if the INK don' flow, the understanding don't grow.
Take some notes, use some lead or ink, consume some scratch paper.
Practice. Don't just read over and look at. DO! Nike. Just DO it.
Worksheet - Oct 21st midterm followup exercise 8 questions.
Turtle Trigonometry exercise. Heading, xcor, ycor, and turtle #1 having similar triangle to turtle #2.
Find the best fitting (smallest "Sum of squares of deviations:")
line
f(x) = mx + b
for the following two points using Data Flyer:
-5 -1 <------ point a
0 3 <------ point b
Now, REFRESH the Data Flyer application and try these three points:
-5 -1 point a (same as before)
0 3 point b (same as before)
-2.5 2 point c <----- ths new 3rd point
Can you get the Sum of squares of deviations: 0.67 or less????
Note: It is helpful to click on "Light Grid Lines"
When you get the 0.67 or less
for the Sum of the squares of the deviations,
after doing enough Change Function and Slider adjusting,
you have discovered your
best fitting function
f(x) = mx + b, or
y = mx + b What is m? What is b?
Know the idea
of the RISE
(the y2 - y1 or y difference
or distance or change)
and
the RUN
(the x difference, x2 - x2,
the x distance or change)
E E R
S S I
I I S
R or R E
R U N R U N R U N
Run across (the x-axis) Rise UP (on the y-axis)
Rise
------ = slope of the line connecting the two points
Run
Netlogo TURTLES randomly scatter, then turn into either a COW or a HOUSE depending on whether they hit the BULLS EYE or missed the oval shaped bulls eye.
Know and understand the formula for coming up with a Monte Carlo estimated area when you know the proportion of or the actual count of "darts" that landed inside the area of interest.
Example: Look at the following diagram which shows a solid point for every dart that was thrown
and where it hit inside the target area. The target area is the rectangle there you see
that goes from x = 1 to x = 3 and from y = 4 to y = 8.
(Note: for practical purposes, only 16 or 20 darts were thrown
in the examples shown here).
Calculate what the estimated area of the region above function g
and below function h would be? (The area BETWEEN function g and function h).
Please show your work and calculations.
I need to see your process of arriving at the result.
You will get partial credit if your equation is correct, but you just had a simple calculation, arithmetic error.
You will NOT get full credit for just having the correct answer, so show the process for that reason too.
