title: Time complexity problem between two different machines
body: <p>I've stuck in a problem below.</p>
  
  <p>A particular algorithm has time complexity T(n) = 3T(n-1) + 1.</p>
  
  <p>So, in asymptotic terms, the above algorithm has time complexity of O(3^n).</p>
  
  <p>That exeucting an implementation of the algorithm on a particular machine X takes t seconds for n inputs.</p>
  
  <p>The question is that, Assume that there is a machine Y which is 27times faster than machine X, how many inputs could Y can process in same t second..?</p>
  
  <p>I can solve this problem in my head ambiguously.. but cannot explain anymore.</p>
  
  <p>Is there a simple way of solving this issue?</p>