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...

Zombies have invaded my lab! They recruit more of the undead at the rate:<br>dz<br>10<br>= f(z) = (z – 6)(z + 6) In(~),<br>dt<br>where t is time and z is the number of zombies.<br>Determine all biologically meaningful steady states (equilibrium points).<br>Determine the stability of each steady state (equlibrium point) that is biologically<br>meaningful, using the derivative test.<br>Draw a phase-line diagram and answer:

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="" "/="">
Extracted 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.="">

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

Extracted 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=""><0, one has that 1 is unstable. in the long term there will be 6 zombies in my lab. %3d one="" has="" that="" 1="" is="" unstable.="" in="" the="" long="" term="" there="" will="" be="" 6="" zombies="" in="" my="" lab.="">

Jun 05, 2022

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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...

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