We find exact inflationary solutions with exit, including exact forms of the potential, by specifying the rate of expansion and using the number of e-foldings as the effective dynamical variable. These include solutions in which the potential drives nearly exponential or power-law inflation for ${\mathit{t}}_{\mathit{i}}$\ensuremath{\le}t${\mathit{t}}_{\mathit{e}}$, and then directs the expansion smoothly towards radiationlike evolution for t\ensuremath{\ge}${\mathit{t}}_{\mathit{e}}$.