In $[4]$: # Run this cell to see how you can use the Python interpreter to calculate an expression like the one above:

$n=\frac{\mathrm{.}01**10000****2}{100}****2$

print$(\text{'}$Answer is: $\text{'},n,\text{'}$ seconds'$)$

Answer is: $100\mathrm{.}0$ seconds

P$4,$ Q$1$: In the cell $($or cells $-$ you can do calculations directly in cells if you want$)$ below determine how long it would take an O$(n**3)$ algorithm to

process $1,000$ inputs if we know that processing $10$ inputs takes $\mathrm{.}001$ seconds. If you calculate in a cell be sure it clearly shows the answer.

Alternately, show the calculation in one cell and the answer in a different Markdown cell. Use the above code as a template if you want to use

Python to do the calculation.

In $[]$:

P$4,$ Q$2$: In the cell $($or cells$)$ below determine how long it would take an $O(2**n)$ algorithm $(2$ to the nth power $-$ exponential$)$ to process $40$ inputs if

we know that processing $10$ inputs takes $\mathrm{.}0001$ seconds. If the answer is large, how many minutes, hours, days, etc. might this require?

In $[]$:

P$4,$ Q$3$: In the cell $($or cells$)$ below determine how long it would take an O$($n Ig n$)$ algorithm to process $100,000$ inputs if we know that processing

$10$ inputs takes $\mathrm{.}0001$ seconds. Since we're dealing with estimates you may assume $"$Ig $10"$ is $3\mathrm{.}15$ and $"$lg $100,000$ is $16\mathrm{.}6.$

In $[]$: