Overview

In this question, you will simulate a population of foxes and rabbits.

You will be required to implement and use functions in your code.

Simulation Math

Imagine a population of Foxes and Rabbits living in an enclosed space. Each

year, some animals are born and some die. Foxes will cause some of the rabbits

to die. If the number of rabbits is too small, some foxes will die from starvation.

This problem can be modeled by writting a program.

At the start of recorded time, there are a starting number of Foxes and Rabbits.

For example, at year $0$

r $=5891$

f $=16$

After one year passes, the number of animals will change. We need to compute

the birth$-$death amount for the year.

The number of rabbits that survive until the next year is given by the follow

formula.

r $+$ br $($A $$ B $$ f$)$c

where

A $=0\mathrm{.}04$

B $=0\mathrm{.}0005$

The symbol bxc means the floor of x$.$ This means we round all values down to

the nearest integer. There is no such thing as $0\mathrm{.}5$ of a fox or rabbit.

Notice that the current number of foxes changes the number of births and deaths.

A similar formula can be created for the foxes. It is affected by the number of

rabbits.

f $$ bf $($G $$ S $$ r$)$c

where

$1$

G $=0\mathrm{.}2$

S $=0\mathrm{.}00005$

The values of A$,$ B$,$ S$,$ and G are based on experimental data.

After $1$ year, the population looks will have

$5891+$ b$5891(0\mathrm{.}040\mathrm{.}000516)$c $=6079$

$16$ b$16(0\mathrm{.}20\mathrm{.}000055891)$c $=18$

After $1$ year, we have $6079$ rabbits and $18$ foxes.

Required Functions

You are required to make and use the following functions in your submission.

def getInteger$($question$)$: Takes as it$$s input parameter a question as a

string. Repeatedly asks the question until it get a positive non$-$zero integer as

input. Return the integer the user entered when successful.

def nextRabbits$($foxes$,$ rabbits$).$ Given a number of foxes and rabbits, returns the number of rabbits in the next year. For example,

nextRabbits$(10,1000)$ will return $1035.$

def nextFoxes$($foxes$,$ rabbits$).$ Given a number of fixes and rabbits, returns

the number of foxes in the next year. For example, nextFoxes$(10,1000)$ will

return $9.$

Main Script

Your main program will ask the user for three integers. They cannot be negative

or zero. If the user enters an invalid input, your program will ask again. It will

only continue when given a valid input.

The three integers are:

$$ The number of rabbits before the start of the simulation $($Year Zero$)$

$$ The number of foxes before the start of the simulation $($Year Zero$)$

$$ The number of years to simulate.

Once you have received the valid inputs, print a table showing the number of

rabbits and foxes over all the years the user asked for. Your table should be well

formatted.

Note: Your table does not need to exaclty match the examples below. You may

change the visuals slightly, but it must be an easy to read and well formatted output.

Example $1$

Enter Number of Rabbits: $1000$

Enter Number of Foxes: $10$

Enter Years to Simulate: $1$

$|$ Years $|$ Foxes $|$ Rabbits $|$

$|-------|-------|-------|$

$|0|10|1000|$

$|1|9|1035|$

Example $2$

Enter Number of Rabbits: $5891$

Enter Number of Foxes: $16$

Enter Years to Simulate: $10$

$|$ Years $|$ Foxes $|$ Rabbits $|$

$|-------|-------|-------|$

$|0|16|5891|$

$|1|18|6079|$

$|2|20|6267|$

$|3|23|6455|$

$|4|26|6638|$

$|5|30|6817|$

$|6|35|6987|$

$|7|41|7144|$

$|8|48|7283|$

$|9|56|7399|$

$|10|66|7487|$

Example $3$

Enter Number of Rabbits: Hats

Invalid Input

Input must be an positive non$-$zero integer

Enter Number of Rabbits: $0$

Invalid Input

Input must be an positive non$-$zero integer

Enter Number of Rabbits: $-2$

Invalid Input

Input must be an positive non$-$zero integer

Enter Number of Rabbits: $999$

Enter Number of Foxes: ghosts

Invalid Input

Input must be an positive non$-$zero integer

Enter Number of Foxes: $12$

Enter Years to Simulate: nine

Invalid Input

$3$

Input must be an positive non$-$zero integer

Enter Years to Simulate: $14$

$|$ Years $|$ Foxes $|$ Rabbits $|$

$|-------|-------|-------|$

$|0|12|999|$

$|1|11|1032|$

$|2|10|1067|$

$|3|9|1104|$

$|4|8|1143|$

$|5|7|1184|$

$|6|7|1227|$

$|7|7|1271|$

$|8|7|1317|$

$|9|7|1365|$

$|10|7|1414|$

$|11|7|1465|$

$|12|7|1518|$

$|13|7|1573|$

$|14|7|1630|$