Case $1$:

As the new manager of a local fitness club, Fitness$-$for$-$fe$,$ you have been studying the club's financial data. You would like to determine how the club's costs behave in order to make accurate predictions for next year. Here is information from the last six months:

$\backslash$table$[[$Month$,\backslash$table$[[$Club Membership$],[($Number of members$)]],$Total Operating Costs,Operating Costs per Member$],[$July$,450,$$$8900,510\mathrm{.}78],[$August$,480,9800,20\mathrm{.}42],[$September$,500,10100,20\mathrm{.}20],[$October$,550,10150,18\mathrm{.}45],[$November$,560,10500,18\mathrm{.}75],[$December$,525,10200,19\mathrm{.}43]]$

Requirements

Use the high$-$low method to determine the club's monthly operating cost equation

Using your answer from Requirement $2,$ predict total monthly operating costs if the club has $600$ members.

Can you predict total monthly operating costs if the club has $3,000$ members?