2. (a) A population of size P (in millions) varies in time t (in years) according to a logistic equation of the form dP
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2. (a) A population of size P (in millions) varies in time t (in years) according to a logistic equation of the form dP
2. (a) A population of size P (in millions) varies in time t (in years) according to a logistic equation of the form dP P(4 - P) dt If the initial population size is P(0) = 1 find the population for all time. [10 Marks) (b) Coffee at a temperature of 60° C is cooling in a room of constant temperature of 20° C. It takes 1 minute for the temperature to reach 50° C. Based on Newton's law of cooling dT = --K(T-20). for some k > 0. find the temperature (1) of the coffee for all time [10 Marks
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