The solution of given differential equation m d v d t = − m g R 2 ( x + R ) 2 is v 0 = 2 g R h R + h .

Question

Question 1. (10 points) A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by dV = 1.45V(2 In(V+1)). dt (a) (4 pts) Find all the equilibria and determine their stability using the stability condition. (b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable. (c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain in biological terms what happens to the size of each of these tumours at time progresses.

Answer 1

Question

Chapter 9.3, Problem 54E

(a)

To determine

To show: The solution of given differential equation mdvdt=−mgR2(x+R)2 is v0=2gRhR+h .

(b)

To determine

To calculate: The escape velocity for the earth.

(c)

To determine

To find: The velocity for R = 3960 miles and g=32ft/s2 .

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