I have a problem understanding an ODE and using it to find something particular. Consider the following :
ODE : dC/dt= S-r*C
S: synthesis rate
r : death rate
Co: initial population
the analystical solution is simply C(t) =S/r -(S/r-Co)*exp(-r*t)
My questions are : i) How can we calculate the population that has died at time t
ii) How can we calculate the population that has synthesized at time t
My problem in understanding is relevant the rates S and r and how these can be applied to evaluate the exact quantity of population that has followed death and generation.
So If I want to find how many have died (or synthesized) at time t (given r or S) is it simply the multiplication with C(t) or with C(t-1)?
I would appreciate your help with this problem. Thanks a lot.