Modeling with Exponential Functions：指数函数模型.doc

Modeling Exponential Data Algebraically and with Computers Population trends in China: The aim of this task is for you to investigate the function that best models the population trends in China from 1950 to 1995. The following table shows the population of China from 1950 to 1995. Note we will choose t = 0 when the year is 1950. Year 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 Population in Millions 554.8 609.0 657.5 729.2 830.7 927.8 998.9 1070.0 1155.3 1220.5 Using technology plot the data points from the above table on an appropriately labelled graph. Comment on any apparent trends shown in the graph. Algebraically develop a linear model and an exponential model that fits the data points on your graph. Plot these developed functions on the graph with the data points and comment on which model fits the original data better. Using technology fit a linear, quadratic and exponential function to the data. Comment on which of these fits the data better and how they compare to the functions you developed. Discuss the implications of each of these models in terms of population growth in China in the future and use each model to predict the population of China in 2011. Here are additional data on population trends in China. Comment on how well each of the models fit the new data. Year 1983 1992 1997 2000 2003 2005 2008 Population in Millions 1030.1 1171.7 1236.3 1267.4 1292.3 1307.6 1327.7 G-Force Tolerance: The goal of this task is to develop a model function the represent the tolerance of human beings to G forces over time. Introduction and background When different forces are applied to an object, “G-force” is a term used to describe the resulting acceleration, and is in relation to acceleration due to gravity (g). Thus a G-force equivalent to twice the force of gravity is 2g (“2 gees”). Astronauts have developed their own terminology, based on sensations. Forward acceleration is often referred to as “eyeballs-in”, where the G-force pushes the body backwar