Does \$\bigcup_{c \ge 1} \mathsf{DTime}(2^{cn})\$ closed under polynomial reduction?

It’s well known $$EXP$$ is closed under polynomial reduction. It means $$\bigcup_{c \ge 1} \mathsf{DTime}(2^{c^{n}})$$ is closed under polynomial reduction. But what about $$\bigcup_{c \ge 1} \mathsf{DTime}(2^{cn})$$? Is it also closed under polynomial reduction?