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CS 121 – Quiz 2

This script demonstrates how to model the populations of rabbits and foxes over time using a loop and mathematical formulas. It begins with essential variable initialization, including constants for growth rates and initial populations, and then executes a loop to calculate yearly population changes based on interactions between the two species. The results are displayed at the end of the simulation. Additionally, another section outlines graphing functions to visualize the populations, highlighting how to combine graphical outputs in a cohesive manner.

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CS 121 – Quiz 2

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  1. CS 121 – Quiz 2 2010 Feb 1st

  2. Question 3 Script Outlines • #it is always beneficial to write “restart” at the beginning of your script to clear all variables • restart: • #Use a, b, g, d to represent alpha, beta, gamma, and delta, which are constants in the formula • a:=0.04; b:=5E-4; g:= 0.2; d:=5E-5; • Cc

  3. Question 3 • #Initial rabbit and fox population • r0:=5486; f0:=15; • #Set a variable “years” to represent the number of years that the model should run, which is also the number of loop • years:=45;

  4. Question3 • #Write a for loop • for i from 1 to years do • #calculate the population in next year next_r := r + floor(r*(a-b*f)); next_f := f – floor(f*(g-d*r)); • #update the rabit and fox population r:=next_r; f:=next_f; • end do; • #print out the population at the end of loop

  5. Question 4 • You might see different graphs in question4, but you can solve it the same way. • You are given a bunch of functions: • g := (t,c) -> plots[display](plottools[line]([t, 0], [t, t+1], color=c)); • gb := (t,c) -> plots[display](plottools[line]([0,t], [t, t+2], color=c)); • f1 := (t,c) -> plots[display](plottools[disk]([t+1,1], color = c)); • ga := (t,c) -> plots[display](plottools[disk]([t+3,1], color = c)); • s := (a,b) -> plots[display]([a(1,red),b(2,blue)], scaling=constrained); • f := (a,b) ->plots[display]([b(-5,red), a(-3,blue)], scaling=constrained);

  6. Question 4 • And also a graph

  7. Question 4 • In order to plot the target graph, you need a red disk and a blue disk first. • #Notice function f1 and ga are perfect to do it. • #Observe where the center of the circle is and the color of the disk • #pass appropriate values to function f1 and ga • f1(1,red) • ga(2,blue)

  8. Question 4 • Then we need to display two disks in the same graph • #Notice function s is to combine 3 graph a and b together • #a takes 2 parameter: 1 and red • #b takes 2 parameters: 2 and blue • #those are the values we plugged in f1 and ga • #so a and b can be substituted by f1 and ga • Finally we came up with the solution • s(f1,ga)

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