Let $P ( t )$ Be the Performance Level of Someone Learning a Skill as Someone

Short Answer

Let $P ( t )$ be the performance level of someone learning a skill as a function of the training time $t$ . The graph of $P$ is called a learning curve. We propose the differential equation
$$\frac { d P } { d t } = r ( E - P ( t ) )$$
as a reasonable model for learning, where $r$ is a positive constant. Solve it as a linear differential equation.