I am creating an iPhone app where I need to show transient confirmation messages (called a toast in Android). For example, when a user submits a comment, I pop up a message saying "thanks for submitting your comment". Shortly after, the message will fade away. There exist many such transient messages all over my iPhone app. I realize that Android and two preset times - "short" and "long", but I'm recreating it on iPhone where I have total control.
What I would like to do is to calculate the optimal time to show each message based off of the number of characters in that message. I want users to have enough time to comfortably read the message, but not so long that the message impedes their usage of the app.
X = number of characters. F(X) = seconds to read entire sentence given X
Is it linear? That is, if it takes 0.5 seconds to read "hello", it would take 1.0 second to read "hello world".
F(X) = 0.1 * X
Does it decay? That is, as people read a long sentence, their reading speed increases?
F(X) = 1 / X
Or is it quadratic? That is, each additional character ads more time than the previous word?
F(X) = X ^ 2