Chapter 6.3, Problem 81E

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

     $N^{\prime }\left(t\right)=\left(t+6\right)e^{-0.25t}$

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?