8. The logistic model is important in the modelling of population dynamics and is represented by N(t) - - (* -1)- where N(t) is the population at some time t (days) No = N(0) is the initial population a and k are positive constants • At t = 0 the population is 5 At one week (t = 7) the population is 10 Eventually after a long time the population is 100 (a) Given these three pieces of information provided about the model, find the exact values of Ng. and k. (b) What is the approximate value of N after two weeks? (c) Approximately after what time was N = 50? (d) Sketch the graph of N(t) (labelling all axes,asymptotes and intercepts).
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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