There are $500$ mice $($M$)$ and $200$ apex predator corgis $($C$)$ released into a field on day $0.$ The

predator$-$prey model that describes the relationship between the mice and corgis is given by the following

system of equations:

$$

$=12$

$$

$=34$

a$)$ In the first equation, in words, what does $1$ represent$/$mean$?$ And $2?($Write $1$ sentence

for each term$).$

b$)$ In the second equation, in words, what does $4$ represent$/$mean$?$ And $3?($Write $1$

sentence for each term$).$

c$)$ Based on your answers from a and b$,$ what term seems to be missing from equation $1?$

Propose a logical mathematical representation for this term using $5.$ Do the same for

equation $2,$ using $6.$

d$)$ Using MATLAB, generate $4$ plots to model the population after $500$ days for each case:

$1234$

Case $1\mathrm{.}02\mathrm{.}0004\mathrm{.}0001\mathrm{.}04$

Case $20\mathrm{.}0002\mathrm{.}0002\mathrm{.}02$

Case $31\mathrm{.}0006\mathrm{.}0006\mathrm{.}06$

Case $4\mathrm{.}2\mathrm{.}00002\mathrm{.}0003\mathrm{.}04$

$($Use a for loop, DO NOT use ode$454$ times$).$ Which term$($s$)$ seems to dominate each

case? Is there a case where no term dominates and they$$re all equally important