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Abstract

The exponential function is one of the most important and widely occurring functions in physics and biology. In biology, it may describe the growth of bacteria or animal populations, the decrease of the number of bacteria in response to a sterilization process, the growth of a tumor, or the absorption or excretion of a drug. (Exponential growth cannot continue forever because of limitations of nutrients, etc.) Knowledge of the exponential function makes it easier to understand birth and death rates, even when they are not constant. In physics, the exponential function describes the decay of radioactive nuclei, the emission of light by atoms, the absorption of light as it passes through matter, the change of voltage or current in some electrical circuits, the variation of temperature with time as a warm object cools, and the rate of some chemical reactions.

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References

  • Banavar, J. R., A. Maritan, A. Rinaldo (1999). Size and form in efficient transportation networks. Nature. 399: 130–132.

    Article  ADS  Google Scholar 

  • Bartlett, A. (2004). The Essential Exponential! For the Future or Our Planet. Lincoln, NE, Center for Science, Mathematics & Computer Education.

    Google Scholar 

  • Berg, M. J., W. G. Berlinger, M. J. Goldberg, R. Spector and G. F. Johnson (1982). Acceleration of the body clearance of phenobarbital by oral activated charcoal. N. Engl. J. Med. 307: 642–644.

    Article  Google Scholar 

  • Clark, V. A. (1975). Survival distributions. Ann. Rev. Biophys. Bioeng. 4: 431–438.

    Article  Google Scholar 

  • Haldane, J. B. S. (1985). On Being the Right Size and Other Essays. Oxford, Oxford University Press.

    Google Scholar 

  • Hemmingsen, A. M. (1960). Energy metabolism as related to body size and respiratory surfaces, and its evolution. Reports of the Steno Memorial Hospital and Nordinsk Insulin Laboratorium 9: 6–110.

    Google Scholar 

  • Kempe, C. H., H. K. Silver, and D. O'Brien (1970). Current Pediatric Diagnosis and Treatment, 2nd ed. Los Altos, CA, Lange.

    Google Scholar 

  • Kozlowski, J. and M. Konarzewski (2004). Is West, Brown and Enquist's model of allometric scaling mathematically correct and biologically relevant? Funct. Ecol. 18: 283–289.

    Article  Google Scholar 

  • Maor, E. (1994). e, The Story of a Number. Princeton, N.J., Princeton University Press

    MATH  Google Scholar 

  • McKee, P. A., W. P. Castelli, P. M. McNamara, and W. B. Kannel (1971). The natural history of congestive heart failure: The Framingham study. New Engl. J. Med. 285: 1441–1446.

    Article  Google Scholar 

  • McMahon, T. (1973). Size and shape in biology. Science 179: 1201–1204.

    Article  ADS  Google Scholar 

  • Murray, J. D. (2001). Mathematical Biology. New York, Springer-Verlag.

    Google Scholar 

  • Peters, R. H. (1983). The Ecological Implications of Body Size. Cambridge, Cambridge University Press.

    Google Scholar 

  • Reich, P. (2001). Body size, geometry, longevity and metabolism: do plant leaves behave like animal bodies? Trends in Ecology and Evolution 16(12): 674–680.

    Article  Google Scholar 

  • Riggs, D. S. (1970). The Mathematical Approach to Physiological Problems. Cambridge, MA, MIT Press.

    Google Scholar 

  • Savage, V. M., J. F. Gillooly, W. H. Woodruff, G. B. West, A. P. Allen, B. J. Enquist, and J. H. Brown (2004). The predominance of quarter-power scaling in biology. Func. Ecol. 18: 257–282.

    Article  Google Scholar 

  • Schmidt-Nielsen, K. (1984). Scaling: Why is Animal Size so Important? Cambridge, Cambridge University Press.

    Google Scholar 

  • West, G. B., J. H. Brown, and B. J. Enquist. (1999). The fourth dimension of life: Fractal geometry and allometric scaling of organisms. Science, 284: 1677–1679. (see also Mackenzie's accompanying editorial on page 1607 of the same issue of Science).

    Article  ADS  MathSciNet  Google Scholar 

  • West, G. B. and J. H. Brown. (2004). Life's universal scaling laws. Physics Today, 57(9): 36–42.

    Article  Google Scholar 

  • White, C. R. and R. S. Seymour. (2003). Mammalian basal metabolic rate is proportional to body mass2/3. Proc. Nat. Acad. Sci. 100(7): 4046-4049.

    Article  ADS  Google Scholar 

  • Zumoff, B., H. Hart, and L. Hellman (1966). Considerations of mortality in certain chronic diseases. Ann. Intern. Med. 64: 595–601.

    Google Scholar 

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Hobbie, R.K., Roth, B.J. (2007). Exponential Growth and Decay. In: Intermediate Physics for Medicine and Biology. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49885-0_2

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