Time complexity: Be sure to show your work. Suppose that a particular algorithm has time complexity T (n) = 10 ∗ 2n, and that execution of the algorithm on a particular machine takes T seconds for n inputs. Now, suppose you are presented with a machine that is 64 times as fast as your current machine. How many inputs can you process on you new machine in T seconds?Suppose that a particular algorithm has time complexity T (n) = 5 ∗ n3, and that execution of the algorithm on a particular machine takes T seconds for n inputs. Now, suppose you are presented with a machine that is 64 times as fast as your current machine. How many inputs can you process on your new machine in T seconds?Suppose that a particular algorithm has time complexity T (n) = 16n, and that execution of the algorithm on a particular machine takes T seconds for n inputs. Now, suppose you are presented with a machine that is 64 times as fast as your current machine. How many inputs can you process on you new machine in T seconds?Bonus:Suppose that computer A executes 1 billion instructions per second, and computer B executes 10 million instructions per second, i. e, Computer A is 100 times faster than computer B in raw computing power. Suppose an expert programmer implements insertion sort in machine language for computer A, and the resulting code requires 2 * n2 instructions to sort n numbers. Suppose an average programmer implements merge sort, using a high-level language on computer B, with the resulting code taking 5 * n *log2n instruction. How long does computer A and computer B take to sort 10 million numbers respectively?