In order for humans to survive our bodies must supply our tissues with oxygen and simultaneously remove carbon dioxide. Compare oxygen and carbon dioxide transfer rates in tissues and vascular components within the human body. How or would these rates differ in a athlete and a smoker?
Theory
- Derivative as an instantaneous rate of change (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 95)
- Diffusion (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 552)
References
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What is the rate of change in the area of habitat, number of endangered species, biomass, etc. over an interval?
Theory
- Derivative as instantaneous rate of change (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 95)
References
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One of the most frequent uses of radiocarbon dating is to estimate the age of organic remains from archaeological sites. When plants fix atmospheric carbon dioxide (CO2) into organic material during photosynthesis they incorporate a quantity of 14C that approximately matches the level of this isotope in the atmosphere (a small difference occurs because of isotope fractionation, but this is corrected after laboratory analysis). After plants die or they are consumed by other organisms (for example, by humans or other animals) the 14C fraction of this organic material declines at a fixed exponential rate due to the radioactive decay of 14C. Comparing the remaining 14C fraction of a sample to that expected from atmospheric 14C allows the age of the sample to be estimated. Find the differential equation that describes this situation. How would you estimate the age of a dinosaur skeleton?
Theory
- Derivatives of exponential function (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 131)
References
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As nuclear power is once again considered as an alternative energy source, it is important to know the decay rate of all of the radioactive materials involved. In a typical Uranium-235 fission event, a U-235 nucleus absorbs a thermal neutron, producing a compound nucleus U-236 in a highly excited state. It is this nucleus, not the U-235 nucleus, that actually undergoes fission, splitting into two fragments. These fragments, between them, emit two neutrons, leaving Xe-140 and Sr-94 as fission fragments. The fragments Xe-140 and Sr-94 are both highly unstable and undergo beta decay (with the emission of an electron) until each reaches a stable end product. Find the differential equations that describe this situation. What is the half-life of this material? What are the long term environmental implications of creating all this radioactive waste?
Theory
- Derivatives of exponential function (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 131)
References
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As urban sprawl continues the amount of contiguous habitat for many organisms is decreased and with it the availability of resources. Compare the change in population size over time for organisms that have access to unlimited resources and space (pre-urbanization) to those that have reduced access to both space and resources (post-urbanization).
Theory
- Exponential population growth (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 358)
- Logistic equation (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 346)
References
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