In this problem, we want to apply a linear function.
We typically see them in the form:
[tex]y=mx+b,[/tex]where m represents the rate of change, and b represents the initial value.
We are given the following information:
• L represents the water value (same as y)
,• d represents the number of days (same as x)
,• 60 represents the original water level (initial value)
,• -0.3 represents the rate at which the wate recedes (rate of change)
Knowing all this information, we can rewrite our equation:
[tex]y=mx+b\rightarrow L=-0.3d+60[/tex]We can graph this using a table, or by using the slope and intercept.
Using a table, we can pick some values for d (days), and find the water level.
Let's find the water level after 0 days, 1 day, 2 days, and 3 days:
[tex]\begin{gathered} L=-0.3(0)+60=60 \\ (0,60) \end{gathered}[/tex][tex]\begin{gathered} L=-0.3(1)+60=59.7 \\ (1,59.7) \end{gathered}[/tex][tex]\begin{gathered} L=-0.3(2)+60=59.4 \\ (2,59.4) \end{gathered}[/tex][tex]\begin{gathered} L=-0.3(3)+60=59.1 \\ (3,59.1) \end{gathered}[/tex]We can put these together in a table, then graph it like this:
To determine when the water level will be at 42 feet, let L = 42:
[tex]\begin{gathered} L=-0.3d+60 \\ \\ 42=-0.3d+60 \end{gathered}[/tex]Subtract 60 from both sides:
[tex]-18=-0.3d[/tex]Divide by -0.3:
[tex]d=60[/tex]It will take 60 days to reach a level of 42.
