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  【Abiologiststudyingfluctuationsinthesizeofaparticularpopulationdecidestoinvestigateamodelforwhichdp/dt=kPcoskt,wherePisthesizeofthepopulationattimetdaysandkisapositiveconstant.(a)Giventhatp=P₀whent=0,expre】

  Abiologiststudyingfluctuationsinthesizeofaparticularpopulationdecidestoinvestigateamodelforwhichdp/dt=kPcoskt,wherePisthesizeofthepopulationattimetdaysandkisapositiveconstant.

  (a)Giventhatp=P₀whent=0,expressPintermsofk,tandP₀

  (b)Findtheratioofthemaximumsizeofthepopulationtotheminimumsize.

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2020-04-2420:32
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洪能国

  dp/dt=kpcoskt

  Separatethevariables:dp/p=k(coskt)dt

  Integratebothsides:lnp=sinkt+c

  p=e^(sinkt+c)=Ce^(sinkt)

  Whent=0,p=Po,therefore,

  Po=Ce^(sin0)=C

  p=Poe^(sinkt)--------AnswerforPart(a)

  Sincee^xisamonotonicallyincreasingfunction,forx1

2020-04-24 20:36:42
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