  In this paper we derive a cosmological model from the $f(R,T)$ theory of
gravity, for which $R$ is the Ricci scalar and $T$ is the trace of the
energy-momentum tensor. We consider $f(R,T)=f(R)+f(T)$, with $f(R)$ being the
Starobinksy model $R+\alpha R^{2}$ and $f(T)=\gamma T$, with $\alpha$ and
$\gamma$ constants. We find that from such a functional form, it is possible to
describe the cosmological scenario of a radiation-dominated universe, which has
shown to be a non-trivial feature within the $f(R,T)$ formalism.
