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

Multiple Choice

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
$\frac { d P } { d t } = r ( G - P ( t ) )$ as a reasonable model for learning, where $r$ is a positive constant. Solve it as a linear differential equation.

A) $P ( t ) = G - C e ^ { - n }$
B) $P ( t ) = G + C e ^ { - n }$
C) $P ( t ) = G + C e ^ { n }$
D) $P ( t ) = G C e ^ { n }$
E) $P ( t ) = G - C e ^ { n }$