Question

The monthly water bill is a function of the number of gallons used. The cost is $19 60 for 20.000 gal or less Over 20.000 gal the cost is $19 60 plus $1 for each 1000 gal over 20,000 with any fraction of 1000 gal charged at a fraction of $1 On what interval is the cost constant? On what interval is the cost increasing? On what interval is the cost constant?

Answer 1

Let's define the monthly water bill as a function, where:

• c ,is the number of gallons consumed that month

,

• B(c), is cost of the monthly water bill

Therefore, for a consumption of 20.000 gallons or less, the monthly water bill would be:

`\begin{gathered} B(c)=19.60 \\ c\le20000 \end{gathered}`

For a consumption of more than 20.000 gallons,

`\begin{gathered} B(c)=19.60+(c-20000)/(1000) \\ c>20000 \end{gathered}`

Therefore:

• The cost is constant ($19.60) when the number of gallons consumed is less than or equal to 20,000 gallons

,

• The cost increases if the number of gallons consumed is greater than 20,000 gallons