How about:

#!/usr/bin/perl -w

use strict;

my @func = ( "b+c(t)+t^234.57*f(t)+Z",
             "a + b + c + t^324*f(t) + t^f(t)",
             "t^123456.3990*f(t) + 4",
             "12 + bt + t^32*f(t)",
             "a+b+c(t)+t^.23*f(t)+Z"        );

foreach (@func) {
    if (/t\^(\d+\.?\d*|\.\d+)\*f\(t\)/) {
        print "$_\n   n = $1\n\n";
    }
}
[download]

Output:

b+c(t)+t^234.57*f(t)+Z
   n = 234.57

a + b + c + t^324*f(t) + t^f(t)
   n = 324

t^123456.3990*f(t) + 4
   n = 123456.3990

12 + bt + t^32*f(t)
   n = 32

a+b+c(t)+t^.23*f(t)+Z
   n = .23
[download]

Note that this will only match one t^n*f(t) per function.