Question

17. (-14 Points DETAILS LARCOLALG10 5.5.036 MY NOTES ASK YOUR TEACHER The management et plastic factory has found that the maximum number of units a worker can produce in a day is 45. The learning curve for the number of its produced per day after a new employee has worked days is modeled by N - 4501 - ." After 20 days on the job, new employee produces 1 unit (a) Find the leaming curve for this employee Cint: First, find the value of L. Round your value of to three decimal places) N- (h) How many days does the model predict wil before this employee is producing 23 units per day (Round your answer to the nearest whole number) days

Answer 1

The Learning curve for the number n of units produced per day after a new employee has worked t days is modeled by N= 45(1-ekt) when t = 20, N= 19. So, 19= 45 45 (1-e20K) 20% 191 20% =) l-e => e I- 19 45 26 95 => 2084 = ln (3) >> &k= zó Ln () → K = - -0.027 -0.027+ I=45(1- 027€) 6 When, N= 23 -0.027+ 23 = 45(-é -0.027 € 23 l-e +) 45 0.027 1- -22-22 > - 0.0274 = Ln ( 22 ) > t = 26 .: The required time is = 126 days