$(1$ point$)$ You are the head of a division of a big Silicon Valley company and have assigned one of your engineers, Jim, the job of devising an algorithm to sort through an English text of n

words and convert it into an Esperanto document. Jim comes up with an algorithm which takes $2$n$2+2$n

bit operations to handle an input text with n words. Suppose the computers in your business can handle one bit operation every nanosecond $(1$

nanosecond $=109$

seconds$).$

$($a$)$ How many nanoseconds would it take Jim's algorithm to convert a text with $14$

words on these computers?

$($b$)$ How many HOURS would it take Jim's algorithm to convert a text with $61$

words on these computers?$($ Do not round your answers for WeBWorK.$)$

$($Recall a million is $106$

$,$ a billion is $109$

and a trillion is $1012$

$.)$

For an input text of $100$

words, the statement that best describes the performance of Jim's algorithm is:

A$.$ His algorithm would take between $40$

thousand and $40$

million years to run.

B$.$ His algorithm would take between $40$

and $400$

years to run.

C$.$ His algorithm would take between $4000$

and $40,000$

years to run.

D$.$ His algorithm would take between $4$

and $40$

years to run.

E$.$ His algorithm would take more than $40$

trillion years to run.

F$.$ His algorithm would take between $40$

billion and $40$

trillion years to run.

G$.$ His algorithm would take between $40$

million and $40$

billion years to run.