Question

If the growth rate of bacteria in a culture medium is directly proportional to the difference between the number of bacteria and a certain optimal number N¯, derive an expression for the number of bacteria n as a function of the time t given that the initial number of bacteria placed in the culture mediam is N0 and that the constant of proportionality is λ. Sketch, by inspection, the graph of n = n(t). How long does it take for the difference in the number of bacteria and the optimal number to reduce to 1 4 of the initial difference?

please could you assist on how to set up the model

Answer 1