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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Out[158]//TableForm=

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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Out[170]//TableForm=

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)