Zombies have invaded my lab! They recruit more of the undead at the rate:dz10= f(z) = (z – 6)(z + 6) In(~),dtwhere t is time and z is the number of zombies.Determine all biologically meaningful steady states (equilibrium points).Determine the stability of each steady state (equlibrium point) that is biologicallymeaningful, using the derivative test.Draw a phase-line diagram and answer: "If 9 zombies are in the lab initially, howmany will there be eventually?"Biologically meaningful steady states are z1 = 6 and z2 = 5. Since f'(6) >0, onehas that 6 is unstable, and since f'(10)<0, one has that 10 is stable. In the longterm there will be 10 zombies in my lab.%3D Biologically meaningful steady states are z1 = 6 and z2 = 10. Since f'(6) <0, onehas that 6 is stable, and since f'(10)>0, one has that 10 is unstable. In the longterm there will be 6 zombies in my lab.%3DBiologically meaningful steady states are z1 = 6 and z2 = 10. Since f'(6) >0, onehas that 6 is stable, and since f'(10)<0, one has that 10 is unstable. In the longterm there will be 6 zombies in my lab.Biologically meaningful steady states are z1 = 1 and z2 = 6. Since f'(6) >0, onehas that 6 is unstable, and since f'(1)<0, one has that 1 is stable. In the long termthere will be 1 zombies in my lab.Biologically meaningful steady states are z1 = 1 and z2 = 6. Since f'(6) <0, onehas that 6 is stable, and since f'(1)<0, one has that 1 is unstable. In the long termthere will be 6 zombies in my lab.%3D

The rate at which Zombies are being recruited to invade the lab is given by the differential…

Zombies have invaded my lab! They recruit more of the undead at the rate: dz 10. = f(z) = (z – 6)(z + 6) ln(==), dt where t is time and z is the number of zombies. Determine all biologically meaningful steady states (equilibrium points). Determine the stability of each steady state (equlibrium point) that is biologically meaningful, using the derivative test. Draw a phase-line diagram and answer: "If 9 zombies are in the lab initially, how many will there be eventually?"

Zombies have invaded my lab! They recruit more of the undead at the rate: dz 10. = f(z) = (z – 6)(z + 6) ln(==), dt where t is time and z is the number of zombies. Determine all biologically meaningful steady states (equilibrium points). Determine the stability of each steady state (equlibrium point) that is biologically meaningful, using the derivative test. Draw a phase-line diagram and answer: "If 9 zombies are in the lab initially, how many will there be eventually?"

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Zombies have invaded my lab! They recruit more of the undead at the rate:
dz
10
= f(z) = (z – 6)(z + 6) In(~),
dt
where t is time and z is the number of zombies.
Determine all biologically meaningful steady states (equilibrium points).
Determine the stability of each steady state (equlibrium point) that is biologically
meaningful, using the derivative test.
Draw a phase-line diagram and answer: "If 9 zombies are in the lab initially, how
many will there be eventually?"
Biologically meaningful steady states are z1 = 6 and z2 = 5. Since f'(6) >0, one
has that 6 is unstable, and since f'(10)<0, one has that 10 is stable. In the long
term there will be 10 zombies in my lab.
%3D

Biologically meaningful steady states are z1 = 6 and z2 = 10. Since f'(6) <0, one
has that 6 is stable, and since f'(10)>0, one has that 10 is unstable. In the long
term there will be 6 zombies in my lab.
%3D
Biologically meaningful steady states are z1 = 6 and z2 = 10. Since f'(6) >0, one
has that 6 is stable, and since f'(10)<0, one has that 10 is unstable. In the long
term there will be 6 zombies in my lab.
Biologically meaningful steady states are z1 = 1 and z2 = 6. Since f'(6) >0, one
has that 6 is unstable, and since f'(1)<0, one has that 1 is stable. In the long term
there will be 1 zombies in my lab.
Biologically meaningful steady states are z1 = 1 and z2 = 6. Since f'(6) <0, one
has that 6 is stable, and since f'(1)<0, one has that 1 is unstable. In the long term
there will be 6 zombies in my lab.
%3D

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