社會學(xué)家認(rèn)識一種現(xiàn)象叫做社會的散布,這是一個(gè)數(shù)據(jù),一種科技的改革傳布 , 或一個(gè)文化的時(shí)尚當(dāng)中人口. 人口的成員能被區(qū)分為二個(gè)班級: 有數(shù)據(jù)的人們和人不. 在大小被知道的固定的人口中,合理的是承擔(dān)人口的散布的比率成比例有數(shù)據(jù)的數(shù)字仍然乘數(shù)字接受它. 如果 X 指示在 N 人的人口中有數(shù)據(jù)的個(gè)體的數(shù)字,那么給社會的散布一個(gè)數(shù)學(xué)的模型藉著 dX/dt=kX(N-X), t 表現(xiàn)時(shí)間和 k 是一個(gè)積極的常數(shù)地方有.
1.解決微分方程式上方和曲線圖的嘗試功能你解決.
2.在數(shù)據(jù)是何時(shí)最快速地傳布?
3.多少人們將會最后得到數(shù)據(jù)?
用翻譯軟件弄得,自己解
一道數(shù)學(xué)建模題,英文的.
一道數(shù)學(xué)建模題,英文的.
Sociologists recognize a phenomenon called social diffusion,which is the spreading of a piece of information,a technological innovation,or a cultural fad amongst a population.The members of the population can be divided into two classes:those who have the information and those who do not.In a fixed population whose size is known,it is reasonable to assume that the rate of diffusion of population is proportional to the number who has the information times the number yet to receive it.If X denotes the number of individuals who have the information in a population of N people,then a mathematical model for social diffusion is given by dX/dt=kX(N-X),where t represents time and k is a positive constant.
1.Solve the differential equation above and try to graph the function you solved.
2.At what time is the information spreading fastest?
3.How many people will eventually receive the information?
Sociologists recognize a phenomenon called social diffusion,which is the spreading of a piece of information,a technological innovation,or a cultural fad amongst a population.The members of the population can be divided into two classes:those who have the information and those who do not.In a fixed population whose size is known,it is reasonable to assume that the rate of diffusion of population is proportional to the number who has the information times the number yet to receive it.If X denotes the number of individuals who have the information in a population of N people,then a mathematical model for social diffusion is given by dX/dt=kX(N-X),where t represents time and k is a positive constant.
1.Solve the differential equation above and try to graph the function you solved.
2.At what time is the information spreading fastest?
3.How many people will eventually receive the information?
英語人氣：526 ℃時(shí)間：2020-04-14 20:09:53
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