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Chemical rate equations The reaction of certain chemical compounds can be modeled using a differential equation of the form y′(t) = –kyn(t), where y(t) is the concentration of the compound for t ≥ 0, k > 0 is a constant that determines the speed of the reaction, and n is a positive integer called the order of the reaction. Assume that the initial concentration of the compound is y(0) = y0 > 0.
a. Consider a first-order reaction (n = 1) and show that the solution of the initial value problem is y(t) = y0e–kt.
b. Consider a second-order reaction (n = 2) and show that the solution of the initial value problem is
c. Let y0 = 1 and k = 0.1. Graph the first-order and second-order solutions found in parts (a) and (b). Compare the two reactions.
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Calculus: Early Transcendentals, Books A La Carte Edition (3rd Edition)
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