Biologists studying an isolated population propose that its rate of change is proportional both to the current population P(t) and to the difference between the carrying capacity M and the current population. Which differential equation family, together with an appropriate restriction on k, most accurately captures this model?
a) dtdP=k(M−P) with k>0
b) dtdP=kP(M−P) with k>0
c) dtdP=kP(M−P) with k<0
d) dtdP=kP(P−M) with k>0