Question: Suppose that instead of continuing to increase at this rate, the bacteria reach a maximum population of \(10^{8}\) and then begin to die off due to lack of food. Assume that for any individual cell that is alive, the chance of dying during the next two hours is \(\frac{1}{3}\)

1. Develop an exponential function that models the size of the population from this point onwards.
2. How long does this model predict that it will take for the population to die out? ( 1 mark)
3. Why might the prediction of this model be wrong? In your answer, give reference to the expected survival probability and discuss its effectiveness in predicting population size as the population gets very small. ( 2 marks)

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