Is there an upper bound of the number of induced subgraphs in a tree (i.e., connected acyclic undirected graph)? The bound can be expressed in terms of vertices, edges, etc.

For example, consider the following graph $G$ represented as edge list: ${(S,T),(T,G),(T,B),(B,H),(H,Q)}$. The number of connected subgraph (i.e., tree) is (represented by the set of vertices): ${S}$, ${T}$, ${G}$, ${B}$, ${S,T}$, ${T,G}$, ${T,B}$, ${S,T,G}$, ${B,T,G}$,${S,T,B}$, ${S,T,G,B}$,

${T,G,B,H}$,${T,B,H,Q}$, ${S,T,B,H}$,${S,T,B,H,G}$,${T,G,B,H,Q}$,${S,T,B,H,Q}$, and

${S,T,B,H,G,Q}$.

I find two seemingly relevant answer that can directly answer my questions 1 and 2 but I’m not sure.