Chapter 4.7, Problem 32E

Learning rate. The rate of change of the probability that an employee learns a task on a new assembly line is

$p^{\prime }\left(t\right)=\frac{1}{t{\left(2+t\right)}^2}$,

Where $p\left(t\right)$ is the probability of learning the task after t months. Find $p\left(t\right)$ given that $p=0.8267\text{ when }t=2$.

$p\left(t\right)=\frac{1}{2\left(2+t\right)}+\frac{1}{4}\text{ In }\left(\frac{t}{2+t}\right)+0.8750$