# 243Review 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)+4

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55 help_outlineImage Transcriptionclose243 Review Exercises A54. Modeling Data The manager of a store recorded the annual sales S (in thousands of dollars) of a product over a period of 7 years, as shown in the table, where t is the time in years, with t= 8 corresponding to 2008. s 49 and 50, sketch the graph of haracteristics. 8 14 t 12 13 10 11 50. f(0) 4, f (6) 0 = 8.1 7.3 12.9 12.8 7.8 9.2 11.3 <0 for x < 2 or (a) Use the regression capabilities of a graphing utility to find a model of the form f'(2) does not exist. f'(4) = 0 S = at +bt2+ ct +d f'(x> O for 2< x< 4 for the data. f"(x) < 0 for x 2 (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 sales states that "The rate of were increasing at the greatest rate. creasing." What does this e graph of the deficit as a think the model would be accurate for predicting (d) Do you future sales? Explain. entory C depends on the o the inventory model Finding a Limit In Exercises 55-64, find the limit, if it exists. 1 - 4x 55. lim 8+ 56. lim x--cox + 1 9x3 + 5 ize the cost, assuming 57. lim 58. lim 7x4 number of units sold for one year, s is the 59. lim G0. lim er of units per order. -2x al defense D (in 61. lim 62. lim are shown in the x+ 2 XIXC xOC 5 corresponding to and Budget) Ok 63. lim 64. lim 0 cos AP Finding Horizontal Asymptotes Using Technology In Exercises 65-68, use a graphing utility to graph the function and identify any horizontal asymptotes. 10 693.5 5x2 66. g(x) = 65. flx) +4 fullscreen
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