The population, P, of kangaroos in a reservation is modelled by the logistic dP dt initially the population of the kangaroos is 15% of the carrying capacity of the equation reservation. 2P (5- P 10 000 ) where t is measured in days. It is estimated that (i) What is the initial population of the kangaroos? (ii) What is the population of the kangaroos when the rate of increase is a maximum?

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