Let x represent the number of days
Let f(x) represent water depth
We can see that the water depth is a function of the number of days.
Water depth, f(x) is the dependent variable and number of days, x is the independent variable.
As the days go by, the water depth changes.
The function is therefore:
[tex]f(x)=54-0.5x[/tex]
The domain is the set of values (number of days) for which the pond will have a valid depth, i.e. between 54'' and 0.
[tex]0\le x\le108[/tex]
Because at 0 days,
[tex]f(x)=54-0.5(0)=54^{\doubleprime}[/tex]
And at 108 days,
[tex]f\mleft(x\mright)=54-0.5\mleft(108\mright)=0[/tex]
