# What is the max. population in the first three months. Suppose that population of certain insects after t months is described as p(t)=4t + (100t)/(t^2+400) + 500.

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The maximum population of certain insects after t months is given as P(t) = `4t + (100*t)/(t^2 + 400) + 500` .

To determine the maximum population after 3 months, substitute t = 3.

P(3) = `4*3 + (100*3)/(3^2 + 400) + 500`

=> `12 + 300/409 + 500`

=> `12 + 0.733 + 500`

=> `512.733`

**As the number of insects is a whole number, the maximum number of insects after 3 months is 512.**