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The table gives the midyear population of Japan, in thousands, from 1960 to 2010.Use a calculator to fit both an exponential function and a logistic function to these data. Graph the data points and both function, and comment on the accuracy of the models. [Hint: Subtract 94,000 from each of the population figures. Then, after obtaining a model from your calculator, add 94,000 to get your final model. It might be helpful to choose $ t = 0 $ to correspond to 1960 or 1980.]

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$P_{E}(t)=1909.7761(1.0796)^{t}+94,000$ and the logistic function$P_{L}(t)=\frac{33,086.4394}{1+12.3428 e^{-0.1657 t}}+94,000 . P_{L}$ is a reasonably accurate

Calculus 2 / BC

Chapter 9

Differential Equations

Section 4

Models for Population Growth

Missouri State University

Harvey Mudd College

Idaho State University

Lectures

13:37

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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The table gives the midyea…

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Population Growth The popu…

because we aren't allowed to show the actual table here. Our goal for this problem is going to be to create a model. So here's what this looks like. We want to first start by um entering data or inputting data. President. Okay, great calculator or Excel. Then you want to select data. Yeah. And create a trend line on trend line. In Excel or aggression line is what it's called the calculator. And then you want to make sure you choose the correct model um um model um form or choose the correct general form. So what I mean by that is going to be it's going to be either a linear form exponential form um Depending on what the problem gives you. And with that form you will obtain the model. And the model is really what we're after. Because once we have the model we can interpret results, predict future outcomes um or determine outcomes of unknown data points. Really that is where modeling becomes a very huge and important aspect within math and science. Um

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