Psychologists have found that, in certain learning situations in which there is a maximum amount that can be learned, the additional amount learned each minute is 30% of the amount yet to be learned at the beginning of that minute. Let 12 units of information be the maximum amount that can be learned.
(a) Find the difference equation for yn, the amount learned after n minutes.
(b) Solve the difference equation from part (a).
(c) Use the solution from part (b) to calculate the amount learned after 6 minutes?