Surge Functions The function x(t) = Ate-rt can be used to model events for which there is a surge and die-off; for example, the sales of a "hot" toy or the incidence of a highly infectious disease. This function can be obtained as the solution of a mass-spring system, m + b + kx = 0. Assume m = 1. Find b and k and initial conditions x(0) and (0) in terms of parameters A and r that would yield the solution shown in Fig. 4.2.20?

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FIGURE 4.2.20 A particular solution to the IVP of Problem 57