Answer:
Practical domain: [tex]v\in[0,230]\ or\ 0\leqslant v\leqslant 230[/tex]
Roger can earn $510 at most when every member of the audience purchases a video
Step-by-step explanation:
The function
[tex]E(v)=50+2v[/tex]
Gives us Roger's earnings when he sells v videos. Knowing the play’s audience consists of 230 people and also each one buys no more than one video, v can take values from 0 to 230 or. equivalently Â
[tex]v\in[0,230]\ ,\ 0\leqslant v\leqslant 230[/tex]
Those limits become the practical domain of E(v) because if we chose v outside of it, the function would lose validity
If nobody is willing to purchase a video, v=0 and Roger's earings would be
[tex]E(0)=50[/tex]
If every person from the audience purchases a video, then v=230 because each person can only purchase 1 video
In that case, where v=230, then
[tex]E(230)=50+2(230)=50+460=510[/tex]
Roger can earn $510 at most.
