Q$2.$ Create a NEW file with the name "part$2".$ Copy the content of the source file in Q$1$ to this file. Modify the program developed for Q$1$ to perform the following tasks:

$-$ Rewrite the function userMenu$()$ such that if the user enters $\text{'}\backslash ($ r $\backslash )\text{'}($or $\text{'}$R$\text{'}),$ it will display "Please enter initial particles $(\backslash (\backslash$mathrm$\{$N$\}$ O $\backslash ))$ : $"$ on the screen. The user should input a positive value of type float and you should create a function inputVal $()$ to handle this. Then, userMenu$()$ will display "Please enter decay constant $($lambda$)$: $"$ on the screen. The user should input a positive value of type float and the function inputVal $()$ should be used. Then, userMenu $()$ should call a function remainPart $()$ which uses the values of $\backslash ($ N$\_\{0\}\backslash )$ and $\backslash (\backslash$lambda $\backslash )$ as input parameters. Function remainPart$()$ will display "Please enter time $($ t $)$: $"$ on the screen. The user should input a positive value of type float and the function inputVal $()$ should be used. Function remainpart $()$ will then display the number of remaining particles $($an integer int$)$ using equation $(1)$ and the percentage to $3$ decimal places. You may use $\backslash (\backslash$exp $(\backslash ))$ function in the math module. The function remainPart $()$ should have no returned value.

$-$ Rewrite the function userMenu$()$ such that if the user enters $\text{'}\backslash ($ h $\backslash )\text{'}($or $\text{'}$H$\text{'}),$ it will display "Please enter decay constant $($lambda$)$: $"$ on the screen. The user should input a positive value of type float and the function inputval $()$ should be used. Then, userMenu $()$ should call a function halflife $()$ which uses the value of $\backslash (\backslash$lambda $\backslash )$ as input parameter. Function halflife$()$ will compute and display the half$-$life of the element by solving equation $(1).$ Note that the half$-$life of an element is the time taken so that the number of remaining particles is exactly half the original number, i$.$e$.,$ it is the time taken for $5000$ particles to decay out of $\backslash ($ N$\_\{0\}\backslash )\backslash (=10000\backslash )$ particles. You may use $\backslash (\backslash$log $(\backslash ))$ function in the math module. The function halflife $()$ should have no returned value. Print the two float outputs to $3$ decimal places, assuming that $1$ year $\backslash (=365\mathrm{.}2422\backslash )$ days.

$-$ Rewrite the function userMenu $()$ such that if the user enters $\text{'}1\text{'}($or $\text{'}\backslash (\text{'}\backslash )\text{'}),$ it will make use of inputval $()$ to get a positive value for $\backslash (\backslash$lambda $\backslash ),$ instead of asking and checking until getting a positive value as in Q$1.$

$-$ 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 a $\text{'}\backslash ($ : $\backslash )\text{'}$ is$/$are entered by the user.

$```$

$[1]$ Find mean lifetime

$[$r$]$ Find remaining particles

$[$h$]$ Find half$-1$ife

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

$[$q$]$ Quit

Please enter your choice $(1,$ r$,$ h$,$ f or q

to quit$)$: r

Please enter initial particles $($N$0)$: $-10$

Input should be positive, please try

again: $0$

Input should be positive, please try

again: $10000$

Please enter decay constant $($lambda$)$: $0\mathrm{.}6$

Please enter time $(\}$t$\backslash$mathrm$\{)$: $2$

Remaining particles after $2\mathrm{.}000$ years is

$3012(30\mathrm{.}119\%)$

$[1]$ Find mean lifetime

$[$r$]$ Find remaining particles

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

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

$[$q$]$ Quit

Please enter your choice $(1,$ r$,$ h$,$ f or q

to quit$)$: H

Please enter decay constant $($lambda$)$: $0$

Input should be positive, please try

again: $0\mathrm{.}4$

Half$-$life is $1\mathrm{.}733$ years $(632\mathrm{.}917$ days$)$

$```$

$```$

$[1]$ Find mean lifetime

$[$r$]$ Find remaining particles

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

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

$[$q$]$ Quit

Please enter your choice $(1,$ r$,$ h$,$ f or q

to quit$)$: q

Thank you for using our system!

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