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Puddy's Auto Shop recently purchnsed a new hydraulic litt, engine crane, and electronic dingnostic equipment. When x represents the number of years the equipment is in use. then the new equipment has an associated rate of savings given by S(x)=65.44=0.3192x2 tens of dollars per year. The equipment also has an operating expense with an associsted rate of cost given by C(x)=0.3192x2+0.16x tens of dollars per yeag, when the equipmert is in use for x yoas. The applot above shows the graph of S(x) in blue and C(x) in rod. Checkboxes A, B, and C will display three dirferent regions with their rospective arbas shaded relaied to this problem. The slider for n wil allow you to control the upper limit for these regions. Use the applot to answer the questions below. (ii) Dotermine how long the new equipment should be usedin order to maxmizo savings and use your answer to complete the senitences below, (iliti: cormpare S to C3 before and after point f in the graphy In order to maximize their savings, Puddy's Auto Shop should use the new equipment for a total of years. At this time, the rate of savings and the rate of cost will both be equal to tens of dollars per year fround to 1 decimal place). Equivalently, the rates of savings and cast are both equal to 5 (cound to the nearest whole dollar). (b) Set up and evaluate the definite integrat to determine the accumulated cost of using the new equipment during the time period determined in part (a). For the last blank, select the cortesponding area given by the definite intogral (the area in the graph that represonts accumulated costs). (c) Set up and evaluate the detivite infogral to determine the accumulated savings of using the new equipment during the time period determined in part (a) For the last biank, select the corresponding area given by the definte integral (the aren in the graph that represents aceumulated savings). (d) Set up and evaluate the definite integral to determine the NET accumulated savings of using the new equipment during the time period determined in part (a) Notice that this answer will also be the moimal possible savings from the new equipenent (again, using the answer from (a) above). For the last blank, seloct the corresponding area given by the definite intogral (the area in the graph that represents the net accumulated savings). Net: Accumulated Savings (round to 1 decimal plase) Note: This answer mhould be oqual to the diflerence between the avswers to parts b) and (ch but could be slightly off dwe fo rounding errer. However, the answer should mateh bhe vake trom the applet (e) Complete the following to interpret the answer from part (d). Aso, to verify that the answer to (d) does indeed give the maximal sasings, compare it to the sarvinga if the equipment is used for more or less time. Convert al net savings amounts to dollars. (Hht Use the applet to compute the requested oomparisona). Pudey's Auto Shop will maximkte their savings when they use the new equpment for a span of years. In this time, Puddy's total net savings will bes If the shop decides to knep using the ecuipment for one addtional year - for a total of years - then the not aavings wit instesd be a fotal of 5 . Similarly, if the equipment is discontinued one year early and only used for years, then the net savings for Rudders Auto shop will tes (a) Detormine how long the new equipment should be used in ortfer to maximize savings and use your answer to complete the sentences below. (Hint: compare 'S' to C before and atter point I in the graph). In crder to maximize their savings, Puddy's Auto Shop should use the new equpment for a total of years. At this time, the rate of savings and the rato of cost will both be equal to tens of dolars per year (round to I decimal place) Equivalently, the rates of savings and cost ane both equal to $ (round to the nearest whole dollar). (b) Set up and evaluate the defince integral to determine the accumulated cost of using the new equipment during the time period detemined in part (ap) For the last blanik, select the comesponding area given by the definite integral (the area in the graph that represonts occumilated oosts). Accumalated Cosks = dx =3 (round to secimal pece) (c) Set up and evaluate the definite integral to dotermine the accumulated savings of using the new equipment during the time period determined in part (a). For the last blank. select the corresponding area glven by the definite integral the area in the graph that represents accumuated savings). Accumulated Savings = dx = (d) Set up and evaluate the definite integral to determine the NET accumulated savings of using the now equipment during the time period determined in part (0) Notice that this answer wil also be the maximal possible savings from the new equpenent (agaln, using the answer from (a) above). For the last blank, select the corresponding area given by the. definite integral (the area in the graph that represents the net accumulated savings). Note: This answer should be equal to the difference between the arswers to parts fo) and (c) but could be slightly off due to rounding error However, the answer should match the valie from the applet. (e) Complete the folowing to interpret the answer from part (d). Also, to verity that the answer to (d) does indeed give the maximal savings, compare at to the savings if the equipment is used for more or less fime. Convert al net savings amounts to dollars. OHint. Use the applot to compute the requested comparisonsy: Puddy's Auto Shop will maximize their sevings when they use the new equpment for a span of years. In this time. Puddy's total net avings will be 5 If the shop decides to keep ising the equipment for one additional year - for a fotal of years - then the net swings will inatead be a total of 5 Similarly, if the equipment is discontinued one year early and only used for years, then the net savings for Puddy's Aato Shop will be s Puddy's Auto Shop recently purchnsed a new hydraulic litt, engine crane, and electronic dingnostic equipment. When x represents the number of years the equipment is in use. then the new equipment has an associated rate of savings given by S(x)=65.44=0.3192x2 tens of dollars per year. The equipment also has an operating expense with an associsted rate of cost given by C(x)=0.3192x2+0.16x tens of dollars per yeag, when the equipmert is in use for x yoas. The applot above shows the graph of S(x) in blue and C(x) in rod. Checkboxes A, B, and C will display three dirferent regions with their rospective arbas shaded relaied to this problem. The slider for n wil allow you to control the upper limit for these regions. Use the applot to answer the questions below. (ii) Dotermine how long the new equipment should be usedin order to maxmizo savings and use your answer to complete the senitences below, (iliti: cormpare S to C3 before and after point f in the graphy In order to maximize their savings, Puddy's Auto Shop should use the new equipment for a total of years. At this time, the rate of savings and the rate of cost will both be equal to tens of dollars per year fround to 1 decimal place). Equivalently, the rates of savings and cast are both equal to 5 (cound to the nearest whole dollar). (b) Set up and evaluate the definite integrat to determine the accumulated cost of using the new equipment during the time period determined in part (a). For the last blank, select the cortesponding area given by the definite intogral (the area in the graph that represonts accumulated costs). (c) Set up and evaluate the detivite infogral to determine the accumulated savings of using the new equipment during the time period determined in part (a) For the last biank, select the corresponding area given by the definte integral (the aren in the graph that represents aceumulated savings). (d) Set up and evaluate the definite integral to determine the NET accumulated savings of using the new equipment during the time period determined in part (a) Notice that this answer will also be the moimal possible savings from the new equipenent (again, using the answer from (a) above). For the last blank, seloct the corresponding area given by the definite intogral (the area in the graph that represents the net accumulated savings). Net: Accumulated Savings (round to 1 decimal plase) Note: This answer mhould be oqual to the diflerence between the avswers to parts b) and (ch but could be slightly off dwe fo rounding errer. However, the answer should mateh bhe vake trom the applet (e) Complete the following to interpret the answer from part (d). Aso, to verify that the answer to (d) does indeed give the maximal sasings, compare it to the sarvinga if the equipment is used for more or less time. Convert al net savings amounts to dollars. (Hht Use the applet to compute the requested oomparisona). Pudey's Auto Shop will maximkte their savings when they use the new equpment for a span of years. In this time, Puddy's total net savings will bes If the shop decides to knep using the ecuipment for one addtional year - for a total of years - then the not aavings wit instesd be a fotal of 5 . Similarly, if the equipment is discontinued one year early and only used for years, then the net savings for Rudders Auto shop will tes (a) Detormine how long the new equipment should be used in ortfer to maximize savings and use your answer to complete the sentences below. (Hint: compare 'S' to C before and atter point I in the graph). In crder to maximize their savings, Puddy's Auto Shop should use the new equpment for a total of years. At this time, the rate of savings and the rato of cost will both be equal to tens of dolars per year (round to I decimal place) Equivalently, the rates of savings and cost ane both equal to $ (round to the nearest whole dollar). (b) Set up and evaluate the defince integral to determine the accumulated cost of using the new equipment during the time period detemined in part (ap) For the last blanik, select the comesponding area given by the definite integral (the area in the graph that represonts occumilated oosts). Accumalated Cosks = dx =3 (round to secimal pece) (c) Set up and evaluate the definite integral to dotermine the accumulated savings of using the new equipment during the time period determined in part (a). For the last blank. select the corresponding area glven by the definite integral the area in the graph that represents accumuated savings). Accumulated Savings = dx = (d) Set up and evaluate the definite integral to determine the NET accumulated savings of using the now equipment during the time period determined in part (0) Notice that this answer wil also be the maximal possible savings from the new equpenent (agaln, using the answer from (a) above). For the last blank, select the corresponding area given by the. definite integral (the area in the graph that represents the net accumulated savings). Note: This answer should be equal to the difference between the arswers to parts fo) and (c) but could be slightly off due to rounding error However, the answer should match the valie from the applet. (e) Complete the folowing to interpret the answer from part (d). Also, to verity that the answer to (d) does indeed give the maximal savings, compare at to the savings if the equipment is used for more or less fime. Convert al net savings amounts to dollars. OHint. Use the applot to compute the requested comparisonsy: Puddy's Auto Shop will maximize their sevings when they use the new equpment for a span of years. In this time. Puddy's total net avings will be 5 If the shop decides to keep ising the equipment for one additional year - for a fotal of years - then the net swings will inatead be a total of 5 Similarly, if the equipment is discontinued one year early and only used for years, then the net savings for Puddy's Aato Shop will be s

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