Chapter 5.5, Problem 36E

Learning Curve The management at a plastics factory has found that the maximum number of units a worker can produce in a day is 30. The learning curve for the number $N$ of units produced per day after a new employee has worked $t$ days is modeled by $N=30\left(1-e^{kt}\right)$. After 20 days on the job, a new employee produces 19 units.

(a) Find the learning curve for this employee. (Hint: First, find the value of $k$.)

(b) How many days does the model predict will pass before this employee is producing 25 units per day?