The management at a certain factory has found that a worker can produce at most 30 units in a day. The learning curve for the number of units N produced per day after a new employee has worked t days is N = 30(1 - e^kt). After 20 days on the job, a particular worker produces 19 units. (a) Find the learning curve for this worker. (b) How many days should pass before this worker is producing 25 units per day?