The "learning curve" describes the rate at which a person learns certain tasks. If a person sets a goal of typing \(N\) words per minute (wpm), the length of time \(t\) (in days) to achieve this goal is given by

\[t=-62.5 \ln \left(1-\frac{N}{80}ight)\]

a. According to this formula, what is the maximum number of words per minute?

b. Solve for \(N\). \(\quad N=80\left(1-e^{-t / 62.5}ight)\)