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CalculusQ&A Library243Review ExercisesA54. Modeling Data The manager of a store recorded theannual sales S (in thousands of dollars) of a product over aperiod of 7 years, as shown in the table, where t is the time inyears, with t= 8 corresponding to 2008.s 49 and 50, sketch the graph ofharacteristics.814t1213101150. f(0)4, f (6)0=8.17.312.912.87.89.211.3 O for 2< x< 4for the data.f"(x) < 0 for x2(b) Use a graphing utility to plot the data and graph the model.(c) Use calculus and the model to find the time t when salesstates that "The rate ofwere increasing at the greatest rate.creasing." What does thise graph of the deficit as athink the model would be accurate for predicting(d) Doyoufuture sales? Explain.entory C depends on theo the inventory modelFinding a LimitIn Exercises 55-64, find the limit, if itexists.1 - 4x55. lim 8+56. limx--cox + 19x3 + 5ize the cost, assuming57. lim58. lim7x4number of units soldfor one year, s is the59. limG0. limer of units per order.-2xal defense D (in61. lim62. limare shown in thex+ 2XIXCxOC5 corresponding toand Budget)Ok63. lim64. lim0 cosAP Finding Horizontal Asymptotes Using TechnologyIn Exercises 65-68, use a graphing utility to graph the functionand identify any horizontal asymptotes.10693.55x266. g(x) =65. flx)+4Question

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