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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
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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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
Transcribed Image Text: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
Transcribed Image Text: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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