# Project Assignment

*label*Humanities

*timer*Asked: Dec 11th, 2017

*account_balance_wallet*$5

**Question description**

just please try answer as you are doing internship right now in the internships, you transitioned from an observer - someone who is learning and watching to acquire knowledge about his or her role and potential for contributions - to a participant, worker and full participant in your internship. Respond to the following questions: When did you transition from observer to participant in your internship? Was there a particular moment or was it gradual? What facilitated the transition? Time, knowledge, trust? What did you do to facilitate the transition? How did you feel as an observer? As a participant? Which was more comfortable and why? How can you maximize your role as a participant? What contributions can, and would, you like to make? What can you do to increase your participation in the internship? Please also respond to one of your peers' comments with an observation of your own about their process or experience in their internship. Be mindful of using constructive or helpful feedback when commenting. T

## Tutor Answer

Attached.

PROJECT 1

Part a

In the predator-prey relationship given, the populations would be modeled by two differential

equations. The Matlab command ode45 will then be used to solve the system of differential

equations. We will consider the predators and the prey as having constant birth and death rates. If

the fox population only feeds on rabbits and has a population of x(t) at time t, when there are no

rabbits at all, the fox population will die out as per the differential x’= -dx where d is the birth

rate less the death rate. The rabbit population y(t) will, with no foxes, continue to increase for

some time as per the differential equation y’=by where b is the birth rate less the death rate. We

would like to model a case where both the populations are positive as per the Lotka-Volterra

system of differential equations, i.e.

x' = (-d + ey)x and x(0) = x0……………….Fox equation

y' = (b - cx)y and y(0) = y0…………………Rabbit equation

we can substitute the above equations in the below Lotka-Volterra system of differential

equations;

x’=0.06x – 0.0004yx

y'= -0.08y + 0.0002xy such that;

x’= (-d+ey)x=0.06x – 0.0004yx. We get d=-0.06 and e =-0.0004

y’=(b-cx)y =(-0.08+0.0002yx). Simplifying we get ...

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