Since it represents a linear function we can model the function like this:
[tex]\begin{gathered} y=mx+b \\ where: \\ y=cost \\ x=amount_{\text{ }}of_{\text{ }}water \\ so: \\ (16,32.67) \\ 32.67=16m+b_{\text{ }}(1) \\ ----- \\ (30,52.97) \\ 52.97=30m+b_{\text{ }}(2) \\ \end{gathered}[/tex]Using elimination:
[tex]\begin{gathered} (2)-(1) \\ 52.97-32.67=30m-16m+b-b \\ 20.3=14m \\ m=\frac{20.3}{14} \\ m=1.45 \\ and \\ b=9.47 \end{gathered}[/tex]Therefore, the function is given by:
[tex]y=1.45x+9.47[/tex]Evaluating for 18 HCF:
[tex]\begin{gathered} y=1.45(18)+9.47 \\ y=26.1+9.47 \\ y=35.57 \\ \end{gathered}[/tex]Answer:
The cost for using 18 HCF of water is $35.57
