Posted on Categories:数学代写, 数学建模

数学代写|数学建模代写Mathematical Modeling代考|Effects of Immigration and Emigration on Population Size

avatest™

avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

数学代写|数学建模代写Mathematical Modeling代考|Effects of Immigration and Emigration on Population Size

If there is immigration into the population from outside at a rate proportional to the population size, the effect is equivalent to increasing the birth rate. Similarly if there is emigration from the population at a rate proportional to the population size, the effect is the same as that of increase in the death rate.

If however immigration and emigration take place at constant rates $i$ and $e$ respectively, Eqn. (3) is modified to
$$\frac{d x}{d t}=b x-d x+i-e=a x+k$$
Integrating Eqn. (7), we get
$$x(t)+\frac{k}{a}=\left(x(0)+\frac{k}{a}\right) e^{a t}$$
The model also applies to growth of populations of bacteria and microorganisms, to the increase of volume of timber in a forest, to the growth of malignant cells etc. In the case of forests, planting of new plants will correspond to immigration and cutting of trees will correspond to emigration.

数学代写|数学建模代写Mathematical Modeling代考|Interest Compounded Continuously

Let the amount at time $t$ be $x(t)$ and let interest at rate $r$ per unit amount per unit time be compounded continuously and then
\begin{aligned} x(t+\Delta t) & =x(t)+r x(t) \Delta t+0(\Delta t), \ \frac{d x}{d t} & =x r ; x(t)=x(0) e^{r t} \end{aligned}
This formula can also be derived from the formula for compound interest
$$x(t)=x(0)\left(1+\frac{r}{n}\right)^{n t}$$
when interest is payable $n$ times per unit time, by taking the limit as $n \rightarrow \infty$.
In fact comparison of Eqns. (9) and (10) gives us two definitions of the transcendental number $e$ viz.
(i) $e$ is the amount of an initial capital of one unit invested for one unit of time when the interest at the unit rate is compounded continuously.
(ii)
$$e=\operatorname{Lt}_{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^n$$
Also from Eqn. (9) if $x(t)=1$, then
$$x(0)=e^{-r t}$$
so that $e^{-t}$ is the present value of a unit amount due one period hence when interest at the rate $r$ per unit amount per unit time is compounded continuously.

数学代写|数学建模代写Mathematical Modeling代考|Effects of Immigration and Emigration on Population Size

$$\frac{d x}{d t}=b x-d x+i-e=a x+k$$

$$x(t)+\frac{k}{a}=\left(x(0)+\frac{k}{a}\right) e^{a t}$$

数学代写|数学建模代写Mathematical Modeling代考|Interest Compounded Continuously

1036/5000

\begin{aligned} x(t+\Delta t) & =x(t)+r x(t) \Delta t+0(\Delta t), \ \frac{d x}{d t} & =x r ; x(t)=x(0) e^{r t} \end{aligned}

$$x(t)=x(0)\left(1+\frac{r}{n}\right)^{n t}$$

(一)$e$是指以单位利率连续复利的情况下，一个单位的初始资本在一个单位时间内投入的金额。
(ii)
$$e=\operatorname{Lt}_{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^n$$

$$x(0)=e^{-r t}$$

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。