The monthly bill is an illustration of linear functions
The function  that relates the number of gallons of water consumed in a month, x, to the total cost of the bill is [tex]c(x) = 22 + 0.003998x[/tex]
The given parameters are:
[tex]Service\ Fee = \$22[/tex]
[tex]y= \$31.02[/tex] ---- Total Charge
[tex]x= 2256[/tex] --- number of gallons
The expression for the total monthly charge (y) is:
[tex]y = Service\ Fee + r\times x[/tex]
Where
r represents the rate per gallon
Substitute known values
[tex]31.02 = 22 + 2256\times r[/tex]
Collect like terms
[tex]31.02 - 22 = 2256\times r[/tex]
[tex]9.02 = 2256\times r[/tex]
Solve for r
[tex]r = \frac{9.02}{2256}[/tex]
[tex]r = 0.003998[/tex]
So, the expression for the total monthly charges is:
[tex]y = Service\ Fee + r\times x[/tex]
Substitute values for Service Fee and r
[tex]y = 22 + 0.003998x[/tex]
Express as a function
[tex]c(x) = 22 + 0.003998x[/tex]
Hence, the required function is: [tex]c(x) = 22 + 0.003998x[/tex]
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