For the following equations;

$x=e^{-{}_{i}t}sint$;$y=e^{-{}_{i}t}cost$;$z={}_{i}t$

$($a$)$ Sketch the flow$-$chart of a program which generates three$-$dimensional curve of these equations

$($b$)$ Write a $m-$script generating a three$-$dimensional curve as the parameter $t$ is varied and;

$($c$)$ Add comments in your m$-$script.

$($d$)$ Run the $m-$script over some range by entering values from $t=0$ to $t=10$ and with;

$(d-i){}_1=-0\mathrm{.}05,{}_1=-0\mathrm{.}05,{}_1=1$

$(d-ii){}_2=-0\mathrm{.}01t,{}_2=-0\mathrm{.}1t,{}_1=2$

$(d-$iii$){}_3=-0\mathrm{.}05t,{}_3=-0\mathrm{.}05t,{}_3=0\mathrm{.}1$

$($e$)$ Show the screenshot of the plot.

$($e$-$i$)$ Add title to the plot.

$($e$-$ii$)$ Add labels for axes

$($e$-$iii$)$ Add legend representing the generated curves