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Fusion cross sections have been measured for $^{12}\mathrm{C}$${+}^{144}$Sm at bombarding energies in the range 46.5\ensuremath{\le}${\mathit{E}}_{\mathrm{lab}}$\ensuremath{\le}75 MeV by off-line observations of x rays and gamma rays emitted in the decay of the evaporation residues and their daughters. Elastic scattering angular distributions for the same system have also been measured in the range 49\ensuremath{\le}${\mathit{E}}_{\mathrm{lab}}$\ensuremath{\le}63 MeV. These data were used to obtain the parameters of an optical-model potential. It was found that a simultaneous description of both elastic scattering and fusion leads to an energy-dependent potential, with its real and imaginary parts connected by a dispersion relation.