the data in the table represents a companys profit based on the number of items produced.\nprofit based on…

the data in the table represents a companys profit based on the number of items produced.\nprofit based on number of items produced\n| items produced (x) | dollars of profit (y) |\n| ---- | ---- |\n| 100 | -70,500 |\n| 200 | 50 |\n| 300 | 50,100 |\n| 400 | 80,300 |\n| 500 | 90,400 |\n| 600 | 78,000 |\nwhich equation best represents the data?\n$y = - 1.026x^{2}+1016.402x - 162075$\n$y = - 1.036x^{2}+1024.771x - 163710$\n$y = 298.214x - 66317.667$\n$y = 196.2x - 18710$

the data in the table represents a companys profit based on the number of items produced.\nprofit based on number of items produced\n| items produced (x) | dollars of profit (y) |\n| ---- | ---- |\n| 100 | -70,500 |\n| 200 | 50 |\n| 300 | 50,100 |\n| 400 | 80,300 |\n| 500 | 90,400 |\n| 600 | 78,000 |\nwhich equation best represents the data?\n$y = - 1.026x^{2}+1016.402x - 162075$\n$y = - 1.036x^{2}+1024.771x - 163710$\n$y = 298.214x - 66317.667$\n$y = 196.2x - 18710$

Answer

Explanation:

Step1: Substitute (x = 100) into each equation

  • For (y=-1.026x^{2}+1016.402x - 162075): [y=-1.026\times(100)^{2}+1016.402\times100 - 162075=-10260 + 101640.2-162075=-70694.8]
  • For (y=-1.036x^{2}+1024.771x - 163710): [y=-1.036\times(100)^{2}+1024.771\times100 - 163710=-10360+102477.1 - 163710=-71592.9]
  • For (y = 298.214x-66317.667): [y=298.214\times100-66317.667=29821.4 - 66317.667=-36496.267]
  • For (y = 196.2x-18710): [y=196.2\times100-18710=19620 - 18710 = 910]

Step2: Substitute (x = 200) into the equations

  • For (y=-1.026x^{2}+1016.402x - 162075): [y=-1.026\times(200)^{2}+1016.402\times200 - 162075=- 41040+203280.4 - 162075 = 1965.4]
  • For (y=-1.036x^{2}+1024.771x - 163710): [y=-1.036\times(200)^{2}+1024.771\times200 - 163710=-41440 + 204954.2-163710= - 396.8]
  • For (y = 298.214x-66317.667): [y=298.214\times200-66317.667=59642.8-66317.667=-6674.867]
  • For (y = 196.2x-18710): [y=196.2\times200-18710=39240 - 18710=20530]

Step3: Substitute (x = 300) into the equations

  • For (y=-1.026x^{2}+1016.402x - 162075): [y=-1.026\times(300)^{2}+1016.402\times300 - 162075=-92340+304920.6 - 162075 = 50505.6]
  • For (y=-1.036x^{2}+1024.771x - 163710): [y=-1.036\times(300)^{2}+1024.771\times300 - 163710=-93240+307431.3 - 163710 = 50481.3]
  • For (y = 298.214x-66317.667): [y=298.214\times300-66317.667=89464.2-66317.667 = 23146.533]
  • For (y = 196.2x-18710): [y=196.2\times300-18710=58860 - 18710 = 40150]

Step4: Compare the results with the table values

The values of (y) from the equation (y=-1.036x^{2}+1024.771x - 163710) are closest to the values in the table for the given (x) - values.

Answer:

(y=-1.036x^{2}+1024.771x - 163710)