TEST BANK FOR An introduction to Ordinary Differential Equations 1st Edition By Robinson J.C.
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Exam (elaborations) TEST BANK FOR An introduction to Ordinary Differential Equations 1st Edition By Robinson J.C. (Solution Manual)
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---338november 20212021/2022A+
- Exercise 1.1 Radioactive isotopes decay at random, with a ¯xed probability 
of decay per unit time. Over a time interval ¢t, suppose that the probability 
of any one isotope decaying is k¢t. If there are N isotopes, how many will 
decay on average over a time interval ¢t? Deduce that 
N(t + ¢t) ¡ N(t) ¼ ¡Nk¢t; 
and hence that dN=dt = ¡kN is an appropriate model for radioactive decay. 
Over a time interval ¢t, Nk¢t isotopes will decay. We then have 
N(t + ¢t) ¡ N(t) = ¡Nk¢t: 
Divi...
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