Chapter 4.5, Problem 102E

Learning Curve A learning curve is a graph of a function $P\left(t\right)$ that measures the performance of someone learning a skill as a function of the training time t. At first, the rate of learning is rapid. Then, as performance increases and approaches a maximal value M, the rate of learning decreases. It has been found that the function

$P\left(t\right)=M-C{e}^{-kt}$

where k and C are positive constants and $C<M$ is a reasonable model for learning.

(a) Express the learning time t as a function of the performance level P.

(b) For s pole-vaulter in training, the learning curve is given by

$P\left(t\right)=20-14e^{-0.024t}$

where $P\left(t\right)$ is the height he is able to pole-vault after t months. After how many months of training is he able to vault 12 ft?

(c) Draw a graph of the learning curve in part (b).