Chapter 4.5, Problem 102E

Learning Curve A learning curve is a graph of a function P(t) 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

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

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

1. (a) Express the learning time t as a function of the performance level P.
2. (b) For a pole-vaulter in training, the learning curve is given by

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

where P(t) 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?

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