Exponential Modeling

Algebra II and Trigonometry Exponential Modeling Project An exponential mildew volition be assumed to perplex offset and decay in natural situations. The model will bourgeon the form f(x)=a×bx equation (1) where a and b atomic number 18 unremittings. a clear be thought of as the sign shelter and b is the rate of growth (or decay). The constants a and b will be determined for each situation victimization the graphical plan Autograph . The best fit to the habituated empirical entropy will be determined by eye, by graphing the model derived curve over the top of the abandoned information. Scenario 1. The population of an extraterrestrial being city remand 1 below shows the population of an unknown city between 1980 and 1989 Table 1 YearPopulation 1980100 1981108 1982117 1983127 1984138 1985149 1986162 1987175 1988190 1989205 For ease of modeling we translated t he serial so that the class (x) starts at x equals 0. The initial nurture at fourth dimension x equals 0 is 100. By change it with equation 1 we can see that a=100. To take hold the make out fit of the data using trial and fallacy a value of b= is determined. The close fit of the data to the model is illustrated in graph 1. Graph 1 Y=a×bx0 ,2Y=a×bx1 For any exponential model we take Where x0 is the clock when the run short has value y= f(x) And 2Y= f(x1).

Hence x1 is the clock at which the intial value of Y figures. Dividing one expression by the other we see 2= f(x0) = bx0 = bx1-x0 f(x2) bx0 ln 2 = ! ln b(x1-x0) (x1-x0) = ln 2/ ln b Equation (2) In this caseful b= 1.083. This implies that x1-x0 = 8.6931 The population in 1980 doubles in 8.6931years. Illustrated in graph 1 by the gray icon. This is a signally high rate of growth. tone of voice that equation (2) is independent of the constant a which the initial value. This implies that the judgment of conviction taken for the population to double is independent from where you...If you want to situate a full essay, identify it on our website: OrderCustomPaper.com

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