Question: A certain mosquito population (M) grows logistically. A differential equation model is given as below: =0.5(1 (M/5000)) Explain the biological meaning of 0.5 and 5000.

A certain mosquito population (M) grows logistically. A differential equation model is given as below:

=0.5(1

(M/5000))

  1. Explain the biological meaning of 0.5 and 5000.
  2. Draw a state space for the above model and plot the change vectors beginning at state points = 1000, and = 3000. Make sure to label the axis and show your change vector calculation steps
  3. If the mosquito population at time, = 2000years was 1000 (i.e, = 1000), use Euler's method to compute the mosquito population at a time = 2000.2years. You can use a step-size of 0.1 year.

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