4.1 导言:指数和对数函数
章节大纲
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Introduction
::导言
Thomas Malthus, an 18th-century researcher, studied the growth of human populations. He observed that human population grows exponentially, which he described as geometrically. He also observed that the resources that humans needed to survive, such as food, were more limited than the growing human population. He concluded that if the human population grew without limitation, it would only be a matter of time before the world's population would be too large to feed itself, causing what has been called a "Malthusian catastrophe."
::Thomas Malthus, 18世纪的研究人员,研究人类人口增长。他观察到人口成倍增长,他将其描述为几何形。他还观察到,人类生存所需要的资源,如食物,比不断增长的人类人口更加有限。他的结论是,如果人类人口不受限制地增长,那么在世界人口规模太大而不能养活自己之前,就只是时间问题了,这导致了所谓的“马尔图斯灾难 ” 。
Malthus's model is commonly called the natural growth model or exponential growth model. In this chapter we will examine the exponential growth model and its inverse function, the logarithmic model. We will also look at special applications of these function families, including compounded interest and the population logistic model.
::马尔萨斯的模型通常被称为自然增长模型或指数增长模型。本章我们将研究指数增长模型及其反函数,即对数模型。我们还将研究这些功能家庭的特殊应用,包括复合兴趣和人口后勤模型。