Zombies have invaded my lab! They recruit more of the undead at the rate: dz 10 f(2) = (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?"

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Chapter2: Second-order Linear Odes
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Zombies have invaded my lab! They recruit more of the undead at the rate:
dz
= f(2) = (z – 6)(z + 6) In(÷),
10
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
and z2 = 10. Since f'(6) > 0, one has that 6 is
6
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 = 6
and z2 = 10. 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
Transcribed Image Text:Zombies have invaded my lab! They recruit more of the undead at the rate: dz = f(2) = (z – 6)(z + 6) In(÷), 10 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 and z2 = 10. Since f'(6) > 0, one has that 6 is 6 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 = 6 and z2 = 10. 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
Biologically meaningful steady states are z1 =
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 = 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.
Transcribed Image Text:Biologically meaningful steady states are z1 = 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 = 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.
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