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A Calculus Module for Modeling Bioaccumulation, Biomagnification, and Elimination of Mercury

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Abstract:

Bioaccumulation is the increase in concentration of a substance in organisms, as they take in contaminated air, water, or food more rapidly than can be eliminated by metabolization and excretion. As pollutants move from one link in the food chain to another they concentrate through the process of biomagnification. Through a module designed for use in an introductory calculus course, students explore these concepts using data derived from research on mercury levels in the environment and aquatic food chain. Students begin by tracking mercury across the food chain-- from algae and bacteria, to insects, small fish, larger fish, and eventually to birds, mammals, and humans. Concentrations and bioacculumation factors are calculated and literature is reviewed for transfer ratios to fetuses and eggs. Students are asked to use their typical weekly consumption of fish to calculate their average daily dosage of mercury per kilogram of body weight. Based on models of absorption of mercury from food, a separable differential equation for mercury elimination in humans and the fraction of total body mercury in blood, a time dependent equation for blood mercury concentration is derived. Students then find their steady-state level of blood mercury concentration and compare this to the U.S. Environmental Protection Agency’s “safe benchmark blood level.”
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Association:
Name: Mathematical Association of America
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http://www.maa.org


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URL: http://citation.allacademic.com/meta/p206252_index.html
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MLA Citation:

Adkins, Frederick. "A Calculus Module for Modeling Bioaccumulation, Biomagnification, and Elimination of Mercury" Paper presented at the annual meeting of the Mathematical Association of America, The Fairmont Hotel, San Jose, CA, Aug 03, 2007 <Not Available>. 2013-12-15 <http://citation.allacademic.com/meta/p206252_index.html>

APA Citation:

Adkins, F. A. , 2007-08-03 "A Calculus Module for Modeling Bioaccumulation, Biomagnification, and Elimination of Mercury" Paper presented at the annual meeting of the Mathematical Association of America, The Fairmont Hotel, San Jose, CA <Not Available>. 2013-12-15 from http://citation.allacademic.com/meta/p206252_index.html

Publication Type: Conference Paper/Unpublished Manuscript
Abstract: Bioaccumulation is the increase in concentration of a substance in organisms, as they take in contaminated air, water, or food more rapidly than can be eliminated by metabolization and excretion. As pollutants move from one link in the food chain to another they concentrate through the process of biomagnification. Through a module designed for use in an introductory calculus course, students explore these concepts using data derived from research on mercury levels in the environment and aquatic food chain. Students begin by tracking mercury across the food chain-- from algae and bacteria, to insects, small fish, larger fish, and eventually to birds, mammals, and humans. Concentrations and bioacculumation factors are calculated and literature is reviewed for transfer ratios to fetuses and eggs. Students are asked to use their typical weekly consumption of fish to calculate their average daily dosage of mercury per kilogram of body weight. Based on models of absorption of mercury from food, a separable differential equation for mercury elimination in humans and the fraction of total body mercury in blood, a time dependent equation for blood mercury concentration is derived. Students then find their steady-state level of blood mercury concentration and compare this to the U.S. Environmental Protection Agency’s “safe benchmark blood level.”

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