Question

3. Suppose that the water level of a lake is 60 feet and that is receding at a rate of 0.3 foot per day.Write an equation for the water level, L, after d days. Then graph the equation.In how many days will the water level be 42 feet?

Answer 1

In this problem, we want to apply a linear function.

We typically see them in the form:

`y=mx+b,`

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:

`y=mx+b\rightarrow L=-0.3d+60`

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:

`\begin{gathered} L=-0.3(0)+60=60 \\ (0,60) \end{gathered}`
`\begin{gathered} L=-0.3(1)+60=59.7 \\ (1,59.7) \end{gathered}`
`\begin{gathered} L=-0.3(2)+60=59.4 \\ (2,59.4) \end{gathered}`
`\begin{gathered} L=-0.3(3)+60=59.1 \\ (3,59.1) \end{gathered}`

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:

`\begin{gathered} L=-0.3d+60 \\ \\ 42=-0.3d+60 \end{gathered}`

Subtract 60 from both sides:

`-18=-0.3d`

Divide by -0.3:

`d=60`

It will take 60 days to reach a level of 42.