Abstract
The exponential function is one of the most important and widely occurring functions in physics and biology. We start with a gentle introduction to exponential growth and decay and show how to analyze exponential data using semilog and log-log plots. More advanced topics include variable rates, clearance, and multiple decay paths. A model for many processes is the combination of input at a fixed rate accompanied by exponential decay. The limits of exponential growth are explored using the logistic equation. The chapter closes with a description of power-law relationships and scaling, including Kleiber’s law relating the metabolic rate to body mass.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Banavar JR, Maritan A, Rinaldo A (1999) Size and form in efficient transportation networks. Nature 399:130–132
Bartlett A (2004) The essential exponential! For the future of our planet. Center for Science, Mathematics & Computer Education, Lincoln
Bennison LJ, Li TK (1976) Alcohol metabolism in American Indians and whites—lack of racial differences in metabolic rate and liver alcohol dehydrogenase. N Engl J Med 294:9–13
Berg MJ, Berlinger WG, Goldberg MJ, Spector R, Johnson GF (1982) Acceleration of the body clearance of phenobarbital by oral activated charcoal. N Engl J Med 307:642–644
Bland EF, White PD (1941) Coronary thrombosis (with myocardial infarction) ten years later. J Am Med Assoc 114(7):1171–1173
Brown JH,
Clark VA (1975) Survival distributions. Ann Rev Biophys Bioeng 4:431–438
Deffeyes KS (2008) Hubbert’s peak: the impending world oil shortage. Princeton University Press, Princeton
Glazier DS (2005) /4-power law’: Variation in the intra- and interspecific scaling of metabolic rate in animals. Biol Rev 80:611–662
Guttman R (1966) Temperature characteristics of excitation in space-clamped squid axons. J Gen Physiol 49:1007–1018. doi:10.1085/jgp.49.5.1007
Hagen
Haldane JBS (1985) On being the right size and other essays. Oxford University Press, Oxford
Hemmingsen AM (1960) Energy metabolism as related to body size and respiratory surfaces, and its evolution. Rep Steno Meml Hosp Nordisk Insul Lab 9:6–110
Kempe CH, Silver HK, O’Brien D (1970) Current pediatric diagnosis and treatment, 2nd edn. Lange, Los Altos
Levy D, Brink S (2005) A change of heart: how the people of Framingham, Massachusetts helped unravel the mysteries of cardiovascular disease. Knopf, New York
Maor E (1994) e, The story of a number. Princeton University Press, Princeton
McKee PA, Castelli WP, McNamara PM, Kannel WB (1971) The natural history of congestive heart failure: the Framingham study. N Engl J Med 285:1441–1446
McMahon T (1973) Size and shape in biology. Science 179:1201–1204
Murray JD (2001) Mathematical biology. Springer, New York
Peters RH (1983) The ecological implications of body size. Cambridge University Press, Cambridge
Reich P (2001) Body size, geometry, longevity and metabolism: do plant leaves behave like animal bodies? Trends Ecol Evol 16(12):674–680
Romer RH (1991) The mathematics of exponential growth—keep it simple. Phys Teach 9:344–345
Riggs DS (1970) The mathematical approach to physiological problems. MIT Press, Cambridge
Schmidt-Nielsen K (1984) Scaling: why is animal size so important? Cambridge University Press, Cambridge
Wang H, Zeng Z-C, Bui T-A, Sonoda E, Takata M, Takeda S, Iliakis G (2001) Efficient rejoining of radiation-induced DNA double-strand breaks in vertebrate cells deficient of genes of the RAD52 epistasis group. Oncogene 20:2212–2224
West GB, Brown JH, Enquist BJ (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)
West GB, Brown JH (2004). Life’s universal scaling laws. Phys Today 57(9):36–42
White CR, Seymour RS (2003) Mammalian basal metabolic rate is proportional to body mass\(^{2/3}.\)
Zumoff B, Hart H, Hellman L (1966) Considerations of mortality in certain chronic diseases. Ann Intern Med 64:595–601
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Hobbie, R., Roth, B. (2015). Exponential Growth and Decay. In: Intermediate Physics for Medicine and Biology. Springer, Cham. https://doi.org/10.1007/978-3-319-12682-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-12682-1_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12681-4
Online ISBN: 978-3-319-12682-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)