Question #19983

2 Answers
Andy Y.
Jun 23, 2017

#P=-(Ce^(kMt))/(1-Ce^(kMt))#

Explanation:

Assuming the #M# is a constant, you would need to first separate the variables so that

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

Integrate both sides of this equation

#int[1/(kP(M-P))]dP =int dt#

#(ln(P)-ln(P-M))/(kM)=t+C#

#ln(P/(P-M))=kMt + C#

Exponentiate both sides with #e#

#e^(ln(P/(P-M)))=e^(kMt + C)#

#P/(P-M)=Ce^(kMt)#

#P=Ce^(kMt)(P-M)#

#P=PCe^(kMt)-Ce^(kMt)#

#P-PCe^(kMt)=-Ce^(kMt)#

#P(1-Ce^(kMt))=-Ce^(kMt)#

#P=-(Ce^(kMt))/(1-Ce^(kMt))#

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