Please help with maths a level question on differentiation and Logs

a scientist is attempting to model the number of insects, N, present in a colony at time t weeks. when t = 0 there are 400 insects and when t = 1 there are 440 insects
a) a scientist assumes that the rate of increase of the number of insects s inversely proportional to the number of insects present at time t
write down a differential equation to model this situation
b) solve this differential equation to find N in terms of t
c) in a revised model it is assumed that dN/dt = N²/3988e^0.2t
solve this differential eq to find N in terms of t

Reply 1

mqb2766

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Original post by LISAmoauter

a scientist is attempting to model the number of insects, N, present in a colony at time t weeks. when t = 0 there are 400 insects and when t = 1 there are 440 insects
a) a scientist assumes that the rate of increase of the number of insects s inversely proportional to the number of insects present at time t
write down a differential equation to model this situation
b) solve this differential equation to find N in terms of t
c) in a revised model it is assumed that dN/dt = N²/3988e^0.2t
solve this differential eq to find N in terms of t