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Representing a function?



How can I define something like the following(which does not work as
written):

b[t_/;(x[k_]<=t<x[k_+1])]:=s[k,t]

I wish to have this mean the following:

b[t_]:=Which[x[1]<=t<x[2],s[1,t],x[2]<=t<x[3],s[2,t],....etc....]

where x[k_]:=numbers[[k]], and numbers is an increasing sequence of
numbers, s[k_,t_] are functions of t indexed with k, defined for t in
the interval {x[k],x[k+1]}.

Any help on this would be appreciated.

Jay H. Wolkowisky
Dept. of Math.
University of Colorado, Boulder
wolkowis@euclid.colorado.edu  





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