A student enrolled in a stenotyping class progressed at a rate of
N'(t) = (t + 10) e-0.1t.
words per minute per week t weeks after enrolling in a 15- week course.
If a student had no knowledge of stenotyping (that is, if the student could stenotype at 0 words per minute) at the beginning of the course, then how many words per minute N(t) would the student be expected to handle t weeks into the course?
How long, to the nearest week, should it take the student to achieve 90 words per minute? How many words per minute should the student be able to handle by the end of the course?