The demand function for a product is given by $p=4000e^{-\frac{q}{4}}.$

$[$a$]$ Desmos or GeoGebra Classic: Plot the $y-$intercept then set the graphing window with $0x20$ and adjust the $y-$axis to ensure the $y-$intercept is clearly visible. Make sure the entire exponential curve is visible.

Then, submit your screenshot, ensuring that the entire exponential curve and the algebra side view are both clearly visible, as shown in the graphing window.

$($b$)$ At what price per unit will the quantity demanded equal $12$ units? $($Round your answer to two decimal places.$)$

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Solve $[$b$]$ using your graphing utility by plotting the relevant point.

Submit a screenshot from your graphing utility, making sure the plotted point is clearly visible, along with the algebra side view.

$[$c$]$ Interpretation: Interpret the plotted point and explain what aspect of it provides the solution to $[$b$].$

$($d$)$ If the price is $$73\mathrm{.}30$ per unit, how many units will be demanded, to the nearest unit? $|$units

Solve $[$d$]$ using your graphing utility by plotting the relevant point.

Submit a screenshot from your graphing utility, making sure the plotted point is clearly visible, along with the algebra side view.

$[$e$]$ Interpretation: Interpret the plotted point and explain what aspect of it provides the solution to $[$d$].$

Please show your work and explain your answers.