More on knowledge of function

Pressure$-$time relationship in a well is given as follows:

$\backslash$table$[[$Time$,$ hr$,1,2,3,4],[$Pressure$,$ psi,$3000,2970,2952\mathrm{.}3,2939\mathrm{.}8]]$

Using linear interpolation, find the pressure in the well at $2\mathrm{.}5$ hours. Assume:

a$)$ You have no knowledge of the relationship between $p$ and $t$

b$)$ You know that the relationship is $p=f(logt)$

c$)$ Explain the disparity in results. The correct relationship is $p=3000-100logt.$