The water watch program is encouraging customers to reduce the amount of water they use each day. the program is selling low-flow showerheads, which use $2$ gallons of water per minute, for $\$54.00$ each.

a family currently has a showerhead that uses $5$ gallons of water per minute and is considering replacing it with one of the low-flow showerheads. the family uses the shower an average of $20$ minutes per day and pays $\$0.002$ per gallon of water.

part a

create a model that can be used to determine the cost savings, in dollars, for the family to purchase and use a low-flow showerhead in terms of the number of days.

then determine the number of days at which the family will start saving money. justify your answer in terms of the context.

enter your answer and justification in the space provided.