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

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