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1. A culture of bacteria increases at a rate that is proportional to the number of bacteria present at that instant. Assuming that the number doubles every 5 hours, a

biomedical engineer can estimate the number of bacteria present at a future time using the differential equation \frac{d y}{d t}=k y where y is the number of bacteria present at time t. (a) Determine the value of k (b) Assuming at time t = 0, y = 1, use Matlab toolbox to calculate and plot the number ofbacteria present y as a function of time t from 0 to 12 hours.

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