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One-Dimensional Differential Equations

  • Daniel Kaplan
  • Leon Glass
Part of the Texts in Applied Mathematics book series (volume 19)

Abstract

A molecular biology student is conducting experiments using radioactive adenosine triphosphate (ATP). The radioactive isotope is P32, which has a half-life of fourteen days. He has been told to complete his experiments within four weeks, before the isotope decays away. Ordinarily, the ATP is stored in a freezer at —20° C. The student believes—incorrectly—that the radioisotope will last longer if the ATP is frozen at —70° C. To test this hypothesis, he takes 1 µ1 of the ATP, containing about 10 µcuries of the P32, and puts it in the —70° freezer. He keeps the remaining 24 µl of the lab’s supply (containing roughly 240 µcuries) in the —20° C freezer. He takes daily readings of the radioactivity by counting the number of radioactive decays from each sample for one minute. After four weeks, his measurements clearly show that the —20° sample has many more counts than the —70° sample (see Figure 4.1). Since each count represents the decay of one atom of P32, the —20° sample is decaying faster than the —70° sample.

Keywords

Differential Equation Marginal Cost Exponential Growth Doubling Time Nonlinear Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Daniel Kaplan
    • 1
  • Leon Glass
    • 1
  1. 1.Department of PhysiologyMcGill UniversityMontréalCanada

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