An isolated island in the Pacific Ocean has been studied for years by a team of

Question

An isolated island in the Pacific Ocean has been studied for years by a team of field biologists. They have discovered that an invasive species of fish has migrated to the region and are now preying upon native fish species. Over the past few months, the biologists have measured the predator and prey numbers and have fit their data to the following polynomials: x(t) = 150000 + 44992t - 5250 t^2 - 524.91 t^3 y(t) = 20 + 59994 t - 0.7t^2 - 699.63 t^3 where x(t) represents the population of prey in the waters off the island coast and y(t) represents the invasive species population. Both functions are only considered valid for the next nine months, so 0

Explanation / Answer

x(t) = 150000+44992t-5250t2-524.91t3: y(t) = 20+59994t-0.7t2-699.93t3

x(0) = 150000 and y(0) = 20

Hence initial populations are 150000 and 20.

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x'(t) =44992-10500t-1574.73t2   : y'(t) = 59994-1.4t-2099.79t2

hence at t=2.97 x is minimum At t = 5.34 y is minimum. Decreases in (0,5.34( and Inc in (5.34,9)

Decreasing in (0,2.97) and Inc in (2.97,9)

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