The following table shows the depth D , in inches, of water in a pond after $d$ days of eva- poration. Find a linear model for depth as a function of days.

A) $D = - 2 d + 795$
B) $D = 793.67 d + - 0.67$
C) $D = - 0.67 d + 793.67$
D) $D = 795 d + - 2$

Question

The following table shows the depth D , in inches, of water in a pond after $d$ days of eva- poration. Find a linear model for depth as a function of days.

A) $D = - 2 d + 795$ 
B) $D = 793.67 d + - 0.67$ 
C) $D = - 0.67 d + 793.67$ 
D) $D = 795 d + - 2$

Quizplus · Accepted Answer

Since we need to find a linear model for depth as a function of days, we need to look for a relationship between the two variables that can be expressed as a linear equation (y = mx + b) where y is the depth and x is the number of days. Looking at the table, we can see that as the number of days increases, the depth decreases. This suggests that there is a negative linear relationship between days and depth.

To find the equation of the line, we need to calculate the slope (m) and y-intercept (b) using two points from the table. Let's use the points (0, 794) and (6, 792) since they are easy to read from the table.

Slope: m = (y2 - y1)/(x2 - x1) = (792 - 794) / (6 - 0) = -0.67

Y-intercept: b = y1 - mx1 = 794 - (-0.67)(0) = 794

Putting it all together, we get the equation:

D = -0.67d + 793.67

The Following Table Shows the Depth D , in Inches ddd

The Following Table Shows the Depth D , in Inches $d$