solve the diff eqn for P dPdt100P p050 t12SolutiondPdt100P p

Solution

dP/dt=100-P, p(0)=50, t=12

dP/(100-P) = dt

take inegration thus

ln(100-P) = - t + C

100- P = K e^-t

P = 100 - K e^-t

at t = 0 P = 50

50 = 100 - K

K = 100 - 50 = 50

P = 100 - 50 e^-t

at t= 12

P = 100 - 50 e^-12 = 99.99969278938233