Q$1.(29$ points total$)$ Rivian, a leading electric vehicle $($EV$)$ manufacturer, is pushing the boundaries of innovation in battery production. By developing advanced manufacturing processes and investing heavily in cutting$-$edge technologies, Rivian has significantly reduced the costs associated with designing and producing batteries for its electric trucks. These improvements have allowed Rivian to reduce the number of components in its battery systems, lowering production costs and improving vehicle efficiency.

Since $2018,$ Rivian has invested heavily in advanced battery manufacturing technologies. These investments have dramatically impacted Rivian$$s battery production costs, which are as follows:

where q is the number of battery units produced.