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The mice population does not grow unrestricted. The capacity and the growth factor determine the maximum amount of mice. This amount does not have to be stable. For example, choose Growth_Factor = 2 and Capacity=50.
Assignment 2
The changing of the population is shown in Births = (Growth_Factor - Restraining)*Mice
The variable Restraining has a negative influence at the net amount of births.
If Restraining > Growth_Factor then net growth is negative. This means that mice disappear from the population (for example by death or moving to another garden). So, death rate is implemented in the model.
If the population stabilizes then the following applies:
Births = 0
(Growth_Factor - Restraining) * Mice = 0
Then Mice = 0 or (Growth_Factor - Restraining) = Growth_Factor - Mice/Capacity = 0
Mice = Growth_Factor * Capacity
If Growth Factor is 0.8 and Capacity = 75 then Mice = 60
RichText Answers {\rtf1\ansi\deff0\deftab254{\fonttbl{\f0\swiss\fcharset0 Arial;}{\f1\fnil\fcharset0 Arial;}{\f2\fnil\fcharset2 Symbol;}{\f3\fnil\fcharset2 WingDings;}}{\colortbl\red0\green0\blue0;\red255\green0\blue0;\red0\green128\blue0;\red0\green0\blue255;\red255\green255\blue0;\red255\green0\blue255;\red128\green0\blue128;\red128\green0\blue0;\red0\green255\blue0;\red0\green255\blue255;\red0\green128\blue128;\red0\green0\blue128;\red255\green255\blue255;\red192\green192\blue192;\red128\green128\blue128;\red0\green0\blue0;}\wptoolsver4\wpprheadfoot1\paperw12240\paperh15840\margl1000\margr1880\margt400\margb400\headery400\footery720\sectd
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\endnhere\sectdefaultcl{\pard{\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0\b Assignment 1\par
{\pntext\f2 \tab}{{\*\pn \pnlvlblt\pnf2\pnhang\pnindent360{\pntxtb{}}{\pntxta}}\ql\wpparid1\li435\fi-435\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 The mice population does not grow unrestricted. The capacity and the growth factor \plain\f1\fs22\cf0 determine the maximum amount of mice. This amount does not have to be stable. For \plain\f1\fs22\cf0 example, choose Growth_Factor = 2 and Capacity=50.\par
}\pard{\ql\wpparid0\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 \par
\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0\b Assignment 2\par
{\pntext\f2 \tab}{{\*\pn \pnlvlblt\pnf2\pnhang\pnindent360{\pntxtb{}}{\pntxta}}\ql\li435\fi-435\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 The changing of the population is shown in Births = (Growth_Factor - Restraining)*Mice\par
{\pntext\f2 \tab}\ql\wpparid2\li435\fi-435\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 The variable Restraining has a negative influence at the net amount of births. \par
{\pntext\f2 \tab}\ql\wpparid1\li435\fi-435\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 If Restraining > Growth_Factor then net growth is negative. This means that mice \plain\f1\fs22\cf0 disappear from the population (for example by death or moving to another garden). So, \plain\f1\fs22\cf0 death rate is implemented in the model.\par
{\pntext\f2 \tab}\ql\wpparid9\li435\fi-435\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 If the population stabilizes then the following applies:\line \plain\f1\fs22\cf0 Births = 0\line \plain\f1\fs22\cf0 (Growth_Factor - Restraining) * Mice = 0\line \plain\f1\fs22\cf0 Then Mice = 0 or (Growth_Factor - Restraining) = Growth_Factor - Mice/Capacity = 0 \line \plain\f1\fs22\cf0 Mice = Growth_Factor * Capacity\line \plain\f1\fs22\cf0 If Growth Factor is 0.8 and Capacity = 75 then Mice = 60\par
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} NewText Model explanation[ Growth factor causes the increase in amount of mature mice if no restrictions are imposed.
In one period from 100 mice 100 mature offspring originates, the growth factor is 1.
The Capacity is the optimal amount of mice that can live in the garden.
The mortality is high when the capacity is small compared to the amount Mice. Then the amount of Mice divided by Capacity is >> 1.
The mortality is small if the Capacity is high compared to the amount Mice. Then the amount of Mice divided by Capacity is << 1.
The relation Mice/Capacity is a measure for the Restraining.
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\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 In one period from 100 mice 100 mature offspring originates, the growth factor is 1. \par
\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 \par
\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 The Capacity is the optimal amount of mice that can live in the garden. \par
\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 The mortality is high when the capacity is small compared to the amount Mice. Then the \plain\f1\fs22\cf0 amount of Mice divided by Capacity is >> 1. \par
\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 The mortality is small if the Capacity is high compared to the amount Mice. Then the amount \plain\f1\fs22\cf0 of Mice divided by Capacity is << 1. \par
\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 \par
\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 The relation Mice/Capacity is a measure for the Restraining. \par
\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 \par
\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 }}
} 6NewText Modeling problem (continuation of Activity 2a) 10 mice live in a garden. Nevertheless there is a limited amount of food. The maximum number of mice the garden can accommodate is called the capacity. Is the size of the garden an effective restraining for mice growth?
Assignment 1
Execute the model by pressing the green Start button . How the graph shows that restrained growth take place?
Find out what is the effect of doubling or halving the initial values. What is your conclusion?
Assignment 2
The size of the garden restrains growth of the population. Which variable in the model shows this?
Explain how the restrained growth is implemented in the model.
Explain why no death rate is implemented in the model.
Predict at which value the population will stabilize if there is 80 young born mice per 100 mice and garden capacity is 75 mice.
Assignment 3
Is this model suitable for describing the development of the mice population? Explain your answer.
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\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 \par
\ql\wpparid1\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0\b Assignment 1\par
{\pntext\f2 \tab}{{\*\pn \pnlvlblt\pnf2\pnhang\pnindent360{\pntxtb{}}{\pntxta}}\qj\wpparid1\li430\fi-430\ri420\sb0\sl\sa0 \plain\f1\fs22\cf0 Execute the model by pressing the green Start button . How the graph shows that \plain\f1\fs22\cf0 restrained growth take place?\par
{\pntext\f2 \tab}\ql\wpparid0\li420\fi-420\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 Find out what is the effect of doubling or halving the initial values. What is your \plain\f1\fs22\cf0 conclusion?\par
}\pard{\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 \par
\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0\b Assignment 2\par
{\pntext\f2 \tab}{{\*\pn \pnlvlblt\pnf2\pnhang\pnindent360{\pntxtb{}}{\pntxta}}\ql\li420\fi-420\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 The size of the garden restrains growth of the population. Which variable in the model \plain\f1\fs22\cf0 shows this? \par
{\pntext\f2 \tab}\ql\wpparid2\li420\fi-420\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 Explain how the restrained growth is implemented in the model.\par
{\pntext\f2 \tab}\ql\wpparid3\li420\fi-420\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 Explain why no death rate is implemented in the model. \par
{\pntext\f2 \tab}\ql\wpparid1\li420\fi-420\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0 Predict at which value the population will stabilize if there is 80 young born mice per \plain\f1\fs22\cf0 100 mice and garden capacity is 75 mice.\par
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\ql\li0\fi0\ri0\sb0\sl\sa0 \plain\f1\fs22\cf0\b Assignment 3\par
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}* NewNotes Notes+ NewNotes Notes / NewRichNotes Notes '
Procedures $ Program -
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