Consequences of the Time Hierarchy Theorem
Let $f(n) = n^{\log n}$. Then $\mathsf{P} \subseteq \mathsf{DTIME}(f(n))$ while $\mathsf{DTIME}(f(2n+1)^3) \subseteq \mathsf{EXP}$.

(Actually, whether this argument works depends on the exact definition of $\mathsf{DTIME}$. If it doesn't, take $f_C(n) = Cn^{\log n}$ and sum over all integer $C&gt;0$.)