need help on this.

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4. [Total 10 points] A certain mosquito population (M) grows logistically. A differential equation model is given as below: M'-05M(1 M) ' ' _5000 i) [2 points] Explain the biological meaning of 0.5 and 5000. ii) [5 points] Draw a state space for the above model and plot the change vectors beginning at state points M = 1000, and M = 3000. Make sure to label the axis and show your change vector calculation steps for full credit. (No need to scale the axis accurately; Just approximate values and vector lengths are acceptable.) iii) [3 points] If the mosquito population at time, t = 2000 years was 1000 (Le, M = 1000), use Euler's method to compute the mosquito population at a time t = 2000.2 years. You can use a step-size of 0.1 year