A student enrolled in an advanced typing class progressed at a rate of

N′(t) = (t + 6)e^-0.25t

words per minute per week t weeks after enrolling in a 15- week course. If a student could type 40 words per minute at the beginning of the course, then how many words per minute N(t) would the student be expected to type t weeks into the course? How long, to the nearest week, should it take the student to achieve the 70-word-per-minute level? How many words per minute should the student be able to type by the end of the course?