Question

I don’t understand the question its asking for the depth at 4 weeks and 9 weeks

Answer 1

Lake depth after 4 weeks: 343.6 ft

Lake depth after 9 weeks: 340.6 ft

Explanation

The relation between time and lake depth is linear. Using the x-variable to represent time and the y-variable to represent the lake depth, we can use the next equation to relate these variables:

`y=mx+b`

where m is the slope and (0, b) is the y-intercept of the line.

The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:

`m=(y_2-y_1)/(x_2-x_1)`

From the table, this line passes through (0, 346) and (2, 344.8), then its slope is:

`m=(344.8-346)/(2-0)=(-1.2)/(2)=-0.6`

From the table, this line passes through (0, 346), then parameter b is 346.

Substituting m = -0.6 and b = 346, the equation of the line is:

`y=-0.6x+346`

Evaluating this line at x = 4, that is, when time = 4 weeks, we get the next depth:

`\begin{gathered} y=-0.6(4)+346 \\ y=-2.4+346 \\ y=343.6\text{ ft} \end{gathered}`

Evaluating the equation of the line at x = 9, that is, when time = 9 weeks, we get the next depth:

`\begin{gathered} y=-0.6(9)+346 \\ y=-5.4+346 \\ y=340.6\text{ ft} \end{gathered}`