Learning Curve
The management of a factory finds that the maximum number of units a worker can produc in a day is 30. The learning curve for the number of units N produced per day after a new employee has worked for t days is modeled by N = 30(1-ekt).
After 20 days on the job, a worker is producing 19 units in a day. How many days should pass before this worker is producing 25 units per day?

Given that The management of a factory finds that the maximum number of units a worker can produc in a day is 30. The learning curve for the number of units N produced per day after a new employee has worked for t days is modeled by

[tex]N= 30(1-e^{kt})[/tex]

t = no of days

When t =20, we have N =19

Substitute to get

[tex]e^{k20} =1-19/30 = 11/30\\k = -0.05017[/tex]

[tex]N= 30(1-e^{-0.05017t})[/tex]

For producing 25 units per day, substitute N =25 and solve for t

[tex]25= 30(1-e^{-0.5017*t})[/tex]

t=35.71

i.e approximately 36 days should pass