The cubic model seems to be a very good fit to me and the correlation coefficient is much higher than that acheived by any other model. One would certainly criticise its validity as a prediction tool for behaviour outside of the data range (extrapolation) but we're not employing it for that purpose. When the additional data is considered we may well be tempted to reconsider our thoughts and look towards the researcher's model, a simplified logistic regression, which the TI-84 also conveniently has as standard.
Regression analysis is essentially a tool for finding the best type of suggested model for a given set of data. One should always attempt to do this by a manual computation first then use the TI-84 to support or better one's attempt.
Claims damages because he didn't get a first