In an ecology experiment, a number of mosquitoes are placed in a container with water and vegetation. The population of mosquitoes, P, increases and can be modelled by the function P(t) = 24 × 40.384 t2 0, where t is the time, in days, since the mosquitoes were places in the container. (a) Find the number of mosquitoes: (i) initially placed in the container; (ii) in the container after 5 days. The maximum capacity of the container is 5000 mosquitoes. (b) Find the number of days until the container reaches its maximum capacity.

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