The expression that can be used to determine the volume of water in a rain barrel after d days if there were 198.6 gallons of water in the barrel and 12.2 gallons are used each day is:
V(d) = 198.6 - 12.2d
where V(d) is the volume of water in the barrel after d days.
This equation is obtained by subtracting the amount of water used each day (12.2 gallons) from the initial volume of water in the barrel (198.6 gallons) for each of the d days.