The sizes of two interacting populations, 21(t) and 22(t), are modelled over a short time frame...

 

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The sizes of two interacting populations, 21(t) and 22(t), are modelled over a short time frame (with time measured in years) by the linear system of differential equations 'A, where A = - [14] and = 11(t) 12(t) (a) Solve this system of differential equations along with the initial conditions 7(0) = [ 1500 1000 [7 marks] = (b) If this model is only valid up to the first positive time tend such that 1(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. [2 marks] (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. The sizes of two interacting populations, 21(t) and 22(t), are modelled over a short time frame (with time measured in years) by the linear system of differential equations 'A, where A = - [14] and = 11(t) 12(t) (a) Solve this system of differential equations along with the initial conditions 7(0) = [ 1500 1000 [7 marks] = (b) If this model is only valid up to the first positive time tend such that 1(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. [2 marks] (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.