What percentage of zombies must die per unit time so that th

What percentage of zombies must die per unit time so that the zombies eventually die off completely and the humans win? Yay! (Hint: You want the rate of change of the zombie population, the dP/dt, to be zero as the zombie population, P, falls to zero, so solve kP(1-(P/M) )-hP=0 for P, with the given values of k and M; then find the value of h that makes P=0 your only solution to this equation.)

Solution

dP/dt = kP(1-(P/M) )-hP

For change in zombie population to be ze/dt has to be zero

=> P( k(1-(P/M) )-h ) = 0

=> either P = 0 or k(1-(P/M) ) - h = 0

=> k( 1 - (P/M) ) = h

=> P/M = 1 - (h/k)

=> P = M( 1 - (h/k) )

We need to find the value for which P becomes zero

=> 1 - (h/k) = 0

=> h = k