T(n) =
 begin{cases}
      Theta(log_{10} n) &, n = $$sum_{k=1}^{[log_{10} n]} k*9^{k-1},n=overline{kunderbrace{8..8}_text{k={log_{10} n}-1} 9}$$ \
       frac{100-x}{100} & 0leq xleq 100 \
      0 & 100leq x
   end{cases}
]