Discrete-time versus continuous-time models. Assume you have a culture of bacter

Question

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, and compare the solutions. (e) When is a discrete-time model appropriate? When is a continuous-time model appropriate?

Explanation / Answer

a. the unit of time is min

in every 10-minute cell divided into 2 identical copies

in every 20 minutes, cell become = 22

after one hour= 26

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