Mathematics for life science , applying Phyton or Matlab in this question. please make sure all the Phyton or Matlab codes are visible. This question was previously solved by Chegg but the codes were restricted and invisible.

The sizes of two interacting populations, x1(t) and x2(t), are modelled over a short time frame (with time measured in years) by the linear system of differential equations x=Ax,whereA=[1447]andx=[x1(t)x2(t)] (a) Solve this system of differential equations along with the initial conditions x(0)=[15001000]. [7marks] (b) If this model is only valid up to the first positive time tend such that x1(tend)=100, find the value of tend rounded to two decimal places. To answer this part of the question, you are required to use technology (e.g., Python or MATLAB/Octave) to find a root of an appropriate function, and you will receive at most 1 out of the 2 available marks if you do this part of the question by trial-and-error. [2marks] (c) If this model is valid until both species become extinct (where "extinction" in this case should be interpreted as meaning both species simultaneously have a population of less than 1), find the positive time, rounded to one decimal place, when this first happens. To answer this part of the question, you may use technology or trial-and-error. [1 mark]