The differential equation describing the dependence of the temperature on time has the following form:
\frac{dT(t)}{dt} = -\kappa (T(t) - T_f),
where \kappa is a positive constant. You need to solve this equation with the initial condition
T(t = 0) = T_i.
Here it is implied that $T_i$, $T_f$, and $\kappa$ are the known constants.
To do so, you will seek for a solution in the form $T(t) = Ae^{\alpha t} + B$.
You need to substitute this expression into the equation and find the values of A, B and \alpha in terms of the known quantities $T_i$, $T_f$ and $\kappa$ (you will also need to use the initial condition).
Make a sketch of the graph of $T(t)$. Show $T_i$ and $T_f$ on it.