Slowdown in making nondeterministic Turing machines deterministic
If this were the case, then we would have P${}={}$NP, since then any polynomial-time NTM could be made into a polynomial-time DTM.
Your question is whether NTIME$(f(n))\subseteq{}$DTIME$(2f(n))$ for any function $f\colon\mathbb N\to\mathbb N$.  For $f\in\omega(n)$, one has DTIME$(2f(n))={}$DTIME$(f(n))$. So in this case, the question boils down to whether NTIME$(f(n))={}$DTIME$(f(n))$ or not. This question seems open.
What is known is that DTIME$(n)\subsetneq{}$NTIME$(n)$, see https://people.math.gatech.edu/~trotter/papers/34.pdf
It is also known that NTIME$(f(n))\subseteq{}$DTIME$(2^{O(f(n))})$, so you can simulate any NTM by a DTM with exponential slowdown.