Look at the photo for reference.

Examine Figure $1,$ which depicts the US energy consumption from $1980$ on in quintillions of Joules per year.

Figure $1$: US energy consumption

$($a$)$ Propose a model structure that describes the dynamics of this growth.

$($b$)$ Draw the corresponding stocks and flows diagram.

$($c$)$ Write the equations of your model.

Hint: S$($t$)=105-83$e$^-0\mathrm{.}186$t

$($d$)$ Does your model reach an equilibrium? If so$,$ what is its value?

$($e$)$ Do you think that this model will be valid even in the not$-$so$-$distant future? If yes, why? If not, why?