Chapter 4.4, Problem 65E

Habit Strength According to work by the psychologist C. L. Hull, the strength of a habit is a function of the number of times the habit is repeated. If $N$ is the number of repetitions and $H\left(N\right)$ is the strength of the habit, then

$H\left(N\right)=1000\left(1-e^{-kN}\right),$

where $k$ is a constant. Find $H\text{'}\left(N\right)$ if $k=0.1$ and the number of times the habit is repeated is as follows.

a. 10

b. 100

c. 1000

d. Show that $H\text{'}\left(N\right)$ is always positive. What does this mean?