Originally Posted by

**Apostolos1234** Hi everyone,

I have a problem understanding an ODE and using it to find something particular. Consider the following :

ODE : dC/dt= S-r*C

where

S: synthesis rate

r : death rate

C: population

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.