Use the table to answer the question.

Question

Day 0 6 10 14
Lake Level (m.) 10 7.42 5.7 3.98
The water level of a lake is receding, and measurements have been recorded in a data table. Use the table to derive an equation of y, the level of the lake x number of days since the original measurement. What is the water level of the lake after 18 days? Round to the nearest hundredth if necessary.

(1 point)
The water level of the lake after 18 days is
meters.

Answer 1

To derive an equation from the given data points, we can use linear regression or find the equation of a line using the points provided.

The points given are:

• (0, 10)
• (6, 7.42)
• (10, 5.7)
• (14, 3.98)

We will calculate the slope (m) first using two points, say (0, 10) and (6, 7.42):

\[ m = \frac{(y_2 - y_1)}{(x_2 - x_1)} = \frac{(7.42 - 10)}{(6 - 0)} = \frac{-2.58}{6} \approx -0.43 \]

Next, we can use the point-slope form of the line equation \(y - y_1 = m(x - x_1)\). Using the point (0, 10):

\[ y - 10 = -0.43(x - 0) \]

This simplifies to:

\[ y = -0.43x + 10 \]

Now we can use this equation to find the water level after 18 days:

\[ y = -0.43(18) + 10 \] \[ y = -7.74 + 10 \] \[ y = 2.26 \]

Thus, the water level of the lake after 18 days is approximately 2.26 meters.