Question #19983

2 Answers
Jun 23, 2017

P=-(Ce^(kMt))/(1-Ce^(kMt))P=CekMt1CekMt

Explanation:

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

1/(kP(M-P)) dP = dt1kP(MP)dP=dt

Integrate both sides of this equation

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

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

ln(P/(P-M))=kMt + Cln(PPM)=kMt+C

Exponentiate both sides with ee

e^(ln(P/(P-M)))=e^(kMt + C)eln(PPM)=ekMt+C

P/(P-M)=Ce^(kMt)PPM=CekMt

P=Ce^(kMt)(P-M)P=CekMt(PM)

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

P-PCe^(kMt)=-Ce^(kMt)PPCekMt=CekMt

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

P=-(Ce^(kMt))/(1-Ce^(kMt))P=CekMt1CekMt