Question

d=dmax (1-e^(-kt))
This equation is the result of integrating an ordinary differential equation. Derive that ODE and the associated initial condition.

Answer 1

Use the equation to calculate dd(t)/dt, and express it in terms of d(t).
dd/dt = -k*dmax e^-kt = -k*(d - dmax)
Let d' = dmax - d
dd'/dt = -kd'
d' + (1/k) dd'/dt = 0
d' at t= 0 = dmax is the initial condition.

Answer 2

thank you...I was able to work through all the steps with your help!