TEST BANK FOR An introduction to Ordinary Differential Equations 1st Edition By Robinson J.C.

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...