Mathematics, 15.12.2020 15:50, machopr
A population of insects increases at the rate of 200 10t 13t2 what is the change in the population of insects between day 0 and day 3
Answers: 2
![\int\limits^3_0 dr = \int\limits^3_0 (200+10t+13t^{2} ). dt\\\\\int\limits^3_0dr =\int\limits^3_0 \, 200dt + \int\limits^3_0 10tdt +\int\limits^3_0{13t^{2} dt\\\\\\\\R = [200t]^3_0 + [5t^{2} ]^3_0 + [\frac{13t^{3} }{3} ]^3_0\\\\R = 200[(3) - (0)] + 5 (3^{2} - 0^{2} ) + \frac{13}{3} [ 3^{3} - 0^{3} ]\\\\R = 200(3) + 5 (9) + \frac{13}{3}(27)\\\\R = 600+45+117\\\\R = 762](/tpl/images/0985/0786/2a2ad.png)
![R = 200t + \frac{10t^2}{2} + \frac{13t^3}{3} [3,0]](/tpl/images/0985/0786/5aac8.png)
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