Discrete-time versus continuous-time models Assume you have a culture of bacteria growing in a petri dish, and each cell

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Discrete-time versus continuous-time models
Assume you have a culture of bacteria growing in a petri dish, and
each cell divides into two identical copies of itself every 10
minutes.
(a) Choose a unit of time, and find the corresponding probability
of cell division.
(b) Write down a discrete-time model which balances the amount of
cells at time t and at time t + △t.
(c) Define the growth rate, and derive the corresponding
continuous-time model.
(d) Solve both the discrete-time and continuous-time models.