3.3 Rates of Change in the Sciences

Mathematica script by Chris Parrish,
cparrish@sewanee.edu

Problems from James Stewart,
"Calculus: Concepts and Contexts,"
Second Edition, Brooks/Cole, 2001

Lactonization

Stewart, Exercise 3.3.16

The following data concerns the lactonization of a certain acid. See Stewart, Exercise 3.3.16, for details.

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 t 0 2 4 6 8 c(t) 0.08 0.057 0.0408 0.0295 0.021

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Use the approximating poynomial to estimate the rates of growth in 1920, 1980, and 1985.

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The reaction is slowing down. It's rate of change is negative.

World Population

Stewart, Exercise 3.3.17

Consider the population of the world over the course of the last century.

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 year 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 world population (in millions) 1650 1750 1860 2070 2300 2560 3040 3710 4450 5280 6070

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Use the approximating poynomial to estimate the rates of growth in 1920, 1980, and 1985.

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Let's check that last result by plotting the associated tangent line on the previous graph.

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Created by Mathematica  (April 19, 2004)