{"id":1180,"date":"2020-11-25T12:51:44","date_gmt":"2020-11-25T17:51:44","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=1180"},"modified":"2021-06-29T10:45:39","modified_gmt":"2021-06-29T14:45:39","slug":"appendix-a-learning-curves-in-the-baii-plus","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/appendix-a-learning-curves-in-the-baii-plus\/","title":{"raw":"Appendix A: Learning Curves in the BAII Plus","rendered":"Appendix A: Learning Curves in the BAII Plus"},"content":{"raw":"The BAII Plus calculator can be used for more than just Business Math.\u00a0 For example, we use power functions to understand learning Curves.\r\n

Example A.1<\/h2>\r\nIn manufacturing a certain part, we find that the initial part takes 176 hours to manufacture, and that there is a 90% learning curve.\r\n
    \r\n \t
  1. Find a power function that shows the time to create the n<\/em>th item as a function of n<\/em>.<\/li>\r\n \t
  2. How much time does it take to manufacture the 144th item?<\/li>\r\n \t
  3. How many items to we need to manufacture before we are down to 50 hours per part?<\/li>\r\n<\/ol>\r\n \r\n\r\nWe are looking for a function of the form:\r\n

    [latex]t_n = t_1 n^b[\/latex]<\/p>\r\nor using your calculator's built in notation [latex] y = ax^b[\/latex]\r\n\r\nWe can find this using the Data worksheet on the calculator, by fitting a power function using the data points given: (1, 176) and (2, 176\u00d70.9)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Step<\/strong><\/td>\r\nTo<\/strong><\/td>\r\nPress<\/strong><\/td>\r\nDisplay<\/strong><\/td>\r\n<\/tr>\r\n
    1<\/td>\r\nSelect Data Worksheet<\/td>\r\n[2ND] [7\/DATA]<\/td>\r\nX01=0<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\nClear old Data<\/td>\r\n[ 2ND] [CE|C]<\/td>\r\nX01=0<\/td>\r\n<\/tr>\r\n
    3<\/td>\r\nEnter two data points<\/td>\r\n[1] [ENTER]<\/td>\r\nX01=1<\/td>\r\n<\/tr>\r\n
    \u2193176 [ENTER]<\/td>\r\nY01=176<\/td>\r\n<\/tr>\r\n
    \u21932 [ENTER]<\/td>\r\nX02=2<\/td>\r\n<\/tr>\r\n
    \u2193176[\u00d7].9 [=][ENTER]<\/td>\r\nY02= 158.4<\/td>\r\n<\/tr>\r\n
    5<\/td>\r\nEnter STAT mode<\/td>\r\n[2ND] [8\/DATA]<\/td>\r\nLIN<\/td>\r\n<\/tr>\r\n
    6<\/td>\r\nGet into PWR mode<\/td>\r\n[2ND] [ENTER]\r\n\r\n[2ND][ENTER]\r\n\r\n[2ND[ENTER]<\/td>\r\nPWR<\/td>\r\n<\/tr>\r\n
    7<\/td>\r\nCheck that you entered data correctly<\/td>\r\n[\u2193]<\/td>\r\nn=2<\/td>\r\n<\/tr>\r\n
    8<\/td>\r\nFind the Power Function<\/td>\r\n\u2193\u2193\u2193\u2193\u2193\u2193\u2193<\/td>\r\na= 176<\/td>\r\n<\/tr>\r\n
    \u2193<\/td>\r\nb= -0.152003093<\/td>\r\n<\/tr>\r\n
    9<\/td>\r\nFind the time for item 144<\/td>\r\n\u2193\u2193 144 [ENTER]<\/td>\r\nX\u2019 = 144<\/td>\r\n<\/tr>\r\n
    \u2193 [CPT]<\/td>\r\nY\u2019 = 82.68655388<\/td>\r\n<\/tr>\r\n
    10<\/td>\r\nFind the number of the item that takes 50 hours<\/td>\r\n50 [ENTER]<\/td>\r\nY\u2019= 50<\/td>\r\n<\/tr>\r\n
    \u2191 [CPT]<\/td>\r\nX\u2019 = 3940.961945<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
      \r\n \t
    1. We have found a and b in the calculator, so we know that we have: [latex]t_n = 176 n^{-0.152003093}[\/latex]<\/li>\r\n \t
    2. The 144th item takes 82.69 hours to manufacture<\/li>\r\n \t
    3. It will take around 50 hours to manufacture the 3941st<\/sup> item.<\/li>\r\n<\/ol>\r\n \r\n

      Your Own Notes<\/h2>\r\n
        \r\n \t
      • Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t
      • These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t
      • Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"1\"]\r\n\r\n ","rendered":"

        The BAII Plus calculator can be used for more than just Business Math.\u00a0 For example, we use power functions to understand learning Curves.<\/p>\n

        Example A.1<\/h2>\n

        In manufacturing a certain part, we find that the initial part takes 176 hours to manufacture, and that there is a 90% learning curve.<\/p>\n

          \n
        1. Find a power function that shows the time to create the n<\/em>th item as a function of n<\/em>.<\/li>\n
        2. How much time does it take to manufacture the 144th item?<\/li>\n
        3. How many items to we need to manufacture before we are down to 50 hours per part?<\/li>\n<\/ol>\n

           <\/p>\n

          We are looking for a function of the form:<\/p>\n

          [latex]t_n = t_1 n^b[\/latex]<\/p>\n

          or using your calculator’s built in notation [latex]y = ax^b[\/latex]<\/p>\n

          We can find this using the Data worksheet on the calculator, by fitting a power function using the data points given: (1, 176) and (2, 176\u00d70.9)<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
          Step<\/strong><\/td>\nTo<\/strong><\/td>\nPress<\/strong><\/td>\nDisplay<\/strong><\/td>\n<\/tr>\n
          1<\/td>\nSelect Data Worksheet<\/td>\n[2ND] [7\/DATA]<\/td>\nX01=0<\/td>\n<\/tr>\n
          2<\/td>\nClear old Data<\/td>\n[ 2ND] [CE|C]<\/td>\nX01=0<\/td>\n<\/tr>\n
          3<\/td>\nEnter two data points<\/td>\n[1] [ENTER]<\/td>\nX01=1<\/td>\n<\/tr>\n
          \u2193176 [ENTER]<\/td>\nY01=176<\/td>\n<\/tr>\n
          \u21932 [ENTER]<\/td>\nX02=2<\/td>\n<\/tr>\n
          \u2193176[\u00d7].9 [=][ENTER]<\/td>\nY02= 158.4<\/td>\n<\/tr>\n
          5<\/td>\nEnter STAT mode<\/td>\n[2ND] [8\/DATA]<\/td>\nLIN<\/td>\n<\/tr>\n
          6<\/td>\nGet into PWR mode<\/td>\n[2ND] [ENTER]<\/p>\n

          [2ND][ENTER]<\/p>\n

          [2ND[ENTER]<\/td>\n

          		PWR<\/td>\n<\/tr>\n
          7<\/td>\nCheck that you entered data correctly<\/td>\n[\u2193]<\/td>\nn=2<\/td>\n<\/tr>\n
          8<\/td>\nFind the Power Function<\/td>\n\u2193\u2193\u2193\u2193\u2193\u2193\u2193<\/td>\na= 176<\/td>\n<\/tr>\n
          \u2193<\/td>\nb= -0.152003093<\/td>\n<\/tr>\n
          9<\/td>\nFind the time for item 144<\/td>\n\u2193\u2193 144 [ENTER]<\/td>\nX\u2019 = 144<\/td>\n<\/tr>\n
          \u2193 [CPT]<\/td>\nY\u2019 = 82.68655388<\/td>\n<\/tr>\n
          10<\/td>\nFind the number of the item that takes 50 hours<\/td>\n50 [ENTER]<\/td>\nY\u2019= 50<\/td>\n<\/tr>\n
          \u2191 [CPT]<\/td>\nX\u2019 = 3940.961945<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
            \n
          1. We have found a and b in the calculator, so we know that we have: [latex]t_n = 176 n^{-0.152003093}[\/latex]<\/li>\n
          2. The 144th item takes 82.69 hours to manufacture<\/li>\n
          3. It will take around 50 hours to manufacture the 3941st<\/sup> item.<\/li>\n<\/ol>\n

             <\/p>\n

            Your Own Notes<\/h2>\n
              \n
            • Are there any notes you want to take from this section? Is there anything you’d like to copy and paste below?<\/li>\n
            • These notes are for you only (they will not be stored anywhere)<\/li>\n
            • Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n
              \n