Question

1. A model for the average achievement of a group of people learning to type is given by: N(t) = 10 + 6lnt for t ≥ 1

where N(t) is the average number of words typed per minute after t hours of instruction and practice.

1. Calculate the average number of words per minute after 10 hours of instruction and practice.                                                                                [1]
2. How long does it take for students to be able to type at 40 words per minute?                                                                                                                     [3]
3. Differentiate to find N'(t) and hence calculate N'(40) .                       [2]

Answer 1

N(t) = 10 +6ln(t) (a) Avg no. of words per minute after 10 hours (t = 10) N(10) = 10 +61n(10) = 23.81 ~ 24 words (b) 40 = 10 + 6ln(t) 5 = ln(t) t = e5 t = 148.4 minute = 148 minutes t t (c) N(t) = 0 +6 = 6 N'(40) = = words per minute