题目

一道数学建模题,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?

提问时间：2021-01-14

答案

社会学家认识一种现象叫做社会的散布,这是一个数据,一种科技的改革传布 , 或一个文化的时尚当中人口. 人口的成员能被区分为二个班级: 有数据的人们和人不. 在大小被知道的固定的人口中,合理的是承担人口的散布的比率成比例有数据的数字仍然乘数字接受它. 如果 X 指示在 N 人的人口中有数据的个体的数字,那么给社会的散布一个数学的模型藉着 dX/dt=kX(N-X), t 表现时间和 k 是一个积极的常数地方有.
1.解决微分方程式上方和曲线图的尝试功能你解决.
2.在数据是何时最快速地传布?
3.多少人们将会最后得到数据?
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