How to model a learning curve logarithmic function? I have the following example:

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. 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

$$P(t)= M - Ce^{-kt}$$
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 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?
I understand the concept, I do not understand the variables. For example, where does $20$ and $14$ comes from? Is is something specific from this sport? So far I suppose that $20$ is considered peak performance and $14$ the starting performance.
Having that in mind I have to model an equation following the same principle but for the following situation:
Anne is trying to improve her typing skills, currently she's capable of typing $34 $ WPM, considering that a very experienced and fast person can type $90$WPM. In this case, I suppose that $P$ represents WPM and t hours of practice.
What would be the function that models the learning curve of this situation?
 A: 
I do not understand the variables. For example, where does 20 and 14 comes from? Is is something specific from this sport?

Indeed, the values of $M$, $C$ and $k$ depend on the particular task (pole-vaulting or typing, in our cases) that is being modeled, and usually they come from empirical data.

So far I suppose that 20 is considered peak performance and 14 the starting performance.

Yes, 20 is the peak performance. But the starting performance is not correct. The starting performance is computed at time $t=0$. So, we get the starting performance from $P(0) = M - Ce^{-k\cdot 0} = M - C$. Therefore, for pole-vaulting, we have $P(0)= 20-14 = 6$.
Regarding the last exercise:

a very experienced and fast person can type 90WPM.

I would translate the above sentence as $$\lim_{t\to\infty}P(t) = \lim_{t\to\infty}M-Ce^{-kt} = 90.$$
By computing the limit, we get $M = 90$.
If you haven't been taught limits, then you can assume that the performance of a very experienced and fast typewriter is the peak performance, thus $M = 90$.
It remains to compute the $C$ and $k$, and I think here some clarification would be helful. The assignment states about Anne that

currently she's capable of typing 34 WPM

What does the "currently" mean, though? Does Anne have any experience at all? If not, then 34WPM is her starting performance (at time $t=0$) and the above information should be translated as
$$\begin{align}
P(0) &= 34\\
\Leftrightarrow\, 90-C &= 34\\
\Leftrightarrow\, C &= 56
\end{align}$$
However, the assignment says that Anne is trying to improve her typing skills, which in my mind implies that she has already trained for some time $t_0 > 0$. Under this view, things become more complex, because it would mean that "currently" refers to $t_0$. Thus,
$$\begin{align}
P(t_0) &= 34\\
\Leftrightarrow\, 90-Ce^{-k\cdot t_0} &= 34\\
\Leftrightarrow\, Ce^{-k\cdot t_0} &= 56
\end{align}$$
In both cases ($t=0$ or $t = t_0$), we have no information about how to compute $k$. In the second case we also cannot compute $C$.
