Posted by **jessica** on Wednesday, March 7, 2012 at 6:13pm.

Could someone explain this question please.

Suppose the population (in thousands of a certain species of insect after t months is described by the function p(t)=4t+ (100t)/(t^2+400) + 500. Determine the maximum population in the first three months.

- Calculus -
**Steve**, Wednesday, March 7, 2012 at 7:25pm
when x is small (as in the interval [0,3]

100t/(t^2+400) is just basically t/4

so, p(t) looks a lot like 4t + t/4 + 500

that's just a line, so the max and min are at the ends of the interval.

- Calculus -
**jessica**, Wednesday, March 7, 2012 at 7:42pm
If I factor it out, it'll be 17t/4 + 500.

then plug in 3

17(3)/4+500=512 x 1000

=512,750.

therefore the population would be 512,750?

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