Suppose that a particular algorithm has time complexity

$$

$($

$$

$)$

$=$

$$

$2$

T$($n$)=$n

$2$

$$ and that executing an implementation of it on a particular machine takes

$$

t seconds for

$$

n inputs. Now suppose that we are presented with a machine that is $64$ times as fast. How many inputs could we process on the new machine in

$$

t seconds?