Q$3.$ Create a NEW file with the name "part$3".$ Copy the content of the source file in Q$2$ to this file. Modify the

program developed for Q $2$ to perform the following tasks:

Rewrite the function userMenu $()$ such that if the user enters $\text{'}$ fF $\text{'}$y$=$mx$+$b where x

and y becomes functions of the input data pairs: time t or number of remaining particles N$.$ In other words,

transform equation $(1)$ so that y is linear on xy$=$mx$+$b x$=$f$($t$)$ and

y$=$g$($N$)$x$=$f$($N$)$ and y$=$g$($t$).$ The process of fitting of a straight line to the set of transformed data is called

linear regression. You can easily compute m and b based on the following formulae to find this best fitting

straight line and then recover N$\_(0)$ and $\backslash$lambda from m and b :

m$=($n$\backslash$sum xy$-(\backslash$sum x$)(\backslash$sum y$))/($n$\backslash$sum x$^(2)-(\backslash$sum x$)^(2)),$b$=(\backslash$sum y$-$m$(\backslash$sum x$))/($n$)$

n

where

$\backslash$sum x$=$ sum of values of x$=$x$\_(1)+$x$\_(2)+$dots$+$x$\_($n$)$

$\backslash$sum x$^(2)=$ sum of values of x$^(2)=$x$\_(1)^(2)+$x$\_(2)^(2)+$dots$+$x$\_($n$)^(2)$

$\backslash$sum y$=$ sum of values of y$=$y$\_(1)+$y$\_(2)+$dots$+$y$\_($n$)$

$\backslash$sum xy$=$ sum of products $=$x$\_(1)$y$\_(1)+$x$\_(2)$y$\_(2)+$dots$+$x$\_($n$)$y$\_($n$)$

The sample outputs given below should be realised by your program on executing it inside Jupyter Notebook

or under any standard well$-$known Python platform. Notice that the character$($s$)$ following $\text{'}$ : $\text{'}$ i$($s$)/($a$)$re entered by

the user. $-$ The sample outputs given below should be realised by your program on executing it inside Jupyter Notebook or under any standard well$-$known Python platform. Notice that the character$($s$)$ following $\text{'}\backslash ($ : $\backslash )\text{'}$ is$/$are entered by the user.

$```$

$[$l$]$ Find mean lifetime $[[$l$]$ Find mean lifetime

$[$r$]$ Find remaining particles $[$r$]$ Find remaining particles

$[$h$]$ Find half$-$life

$[$f$]$ Find best fitting curve from data

$[$q$]$ Quit

Please enter your choice $($ l$,$ r$,$ h$,$ f or q

to quit$)$: f

Number of data points: $4$

t$1$: $1$

N$1$: $5800$

t$2$: $2$

N$2$ : $2750$

t$3$: $3$

N$3$: $1300$

t$4$: $3\mathrm{.}5$

N$4$: $900$

Initial particles $=12224$

Decay constant $=0\mathrm{.}746$

$[$r$]$ Find remaining

$[$f$]$ Find best fitting curve from data

$[$q$]$ Quit

Please enter your choice $($l$,$ r$,$ h$,$ f or q

to quit$)$: q

Thank you for using our system!

$```$