W := t -> r * 2^(r*t/ RTT);

> W(0);
                                       r

> W(RTT);
                                        r
                                     r 2

> W(2*RTT);
                                      (2 r)
                                   r 2

> W(3*RTT);
                                      (3 r)
                                   r 2

> W(k*RTT);
                                      r    k
                                   r 2  * 2

====================================================

> rsolve( {w(n) = w(n-1) + 2^rho - 1, w(1) = rho}, w(k));
                                   r                 r
                        r + (-1 + 2 ) (k + 1) + 1 - 2

> simplify(%);
                                          r
                                 r - k + 2  k

> g :=  unapply(%, k);
                                               r
                            g := k -> r - k + 2  k