One-Dimensional Differential Equations
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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.
KeywordsDifferential Equation Marginal Cost Exponential Growth Doubling Time Nonlinear Differential Equation
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