Given the information, we know that the tank starts holding 18000 gallons of water. Then after 1 day passes, the tank now holds 18000-450=17550 gallons of water. With this, we can find the slope and the equation required:
[tex]\begin{gathered} (0,18000),(1,17550) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{17550-18000}{1-0}=-\frac{450}{1}=-450 \end{gathered}[/tex]Now, using y=mx+b, we have the following equation:
[tex]y=-450x+18000[/tex]Finally, to know how long will it take to reach 6000 gallons, we make y=6000 and solve for x:
[tex]\begin{gathered} y=6000 \\ \Rightarrow6000=-450x+18000 \\ \Rightarrow450x=18000-6000=12000 \\ \Rightarrow x=\frac{12000}{450}=26.67 \\ x=26.67 \end{gathered}[/tex]Therefore, it will take 26.67 days to reach 6000 gallons of water
