一道数学建模题,英文的.
Sociologistsrecognizeaphenomenoncalledsocialdiffusion,whichisthespreadingofapieceofinformation,atechnologicalinnovation,oraculturalfadamongstapopulation.Themembersofthepopulationcanbedividedintotwoclasses:thosewhohavetheinformationandthosewhodonot.Inafixedpopulationwhosesizeisknown,itisreasonabletoassumethattherateofdiffusionofpopulationisproportionaltothenumberwhohastheinformationtimesthenumberyettoreceiveit.IfXdenotesthenumberofindividualswhohavetheinformationinapopulationofNpeople,thenamathematicalmodelforsocialdiffusionisgivenbydX/dt=kX(N-X),wheretrepresentstimeandkisapositiveconstant.
1.Solvethedifferentialequationaboveandtrytographthefunctionyousolved.
2.Atwhattimeistheinformationspreadingfastest?
3.Howmanypeoplewilleventuallyreceivetheinformation?