Let the (logistic) differential equation be dP/dt=0.004*P(50-P) Find:

Let the (logistic) differential equation be

dP/dt=0.004*P(50-P)

Find:

A)The growth coefficient k=

B)The carrying capacity M=

C)The value of the population P when the rate of population growth starts to slow down Pip=

Sketch (you do not need to solve the IVP to answer this question). Clearly show the main features of the graph (the (0,P(0)) point, the inflection point if any and the asymptote) on your sketch.

D) The graph of the solution for the initial condition P(0)=10

E) The graph of the solution for the initial condition P(0)=70

F) P(t)=

G) Compute P(20)=

Last question, don't worry!

dp 0.004 p 50 p dtdp 0.004 p p 1 dt 50 50 p 0.00008 p 1 50 logistic equation :Given that dpp rp 1 dtk A The growth coefficient k 50 B The carrying capacity M 0.00008 Cdp 0.004 p 50 p dtdp...