Does $DTIME(2^n)$ contain $NSPACE(n)$ ?
Generally, for functions $f(n) \in \Omega(\log(n))$, we have that
$$
 \mathrm{NSPACE}(f) \subseteq \mathrm{DTIME}(2^{O(f)})
$$
A proof can be found on slide 28 onwards of the slide set from:

 http://www.informatik.uni-leipzig.de/alg/lehre/ws12_13/KOMPL/folien-eng.pdf


I don't know if $\mathrm{NSPACE}(n) \subseteq \mathrm{DTIME}(2^{n})$ is true. TSP is in $\mathrm{NSPACE}(n)$, but the best deterministic algorithm known is in $ \mathrm{DTIME}(n^22^{n})$ (as far as I know).