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. $$\begin{array} { | l | l | l | l | l | }
\hline d & 2 & 4 & 6 & 8 \
\hline D & 766 & 764 & 762 & 760 \
\hline
\end{array}$$
A) $D = - 2 d + 770$
B) $D = 768 d + - 1$
C) $D = - 1 d + 768$
D) $D = 770 d + - 2$

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. $$\begin{array} { | l | l | l | l | l | } 
\hline d & 2 & 4 & 6 & 8 \
\hline D & 766 & 764 & 762 & 760 \
\hline
\end{array}$$
A) $D = - 2 d + 770$
B) $D = 768 d + - 1$
C) $D = - 1 d + 768$
D) $D = 770 d + - 2$

Quizplus · Accepted Answer

To find a linear model, we need to find the equation of a line that fits the given data points. Using the two-point form of a line, we can find the equation given two points on the line. Let's use the first and last points, (2,766) and (8,760). The slope of the line is:

\begin{align*}
m &= \frac{\Delta D}{\Delta d} \
  &= \frac{760 - 766}{8 - 2} \
  &= -1
\end{align*}

Now we can use the point-slope form of a line to find the equation of the line:

\begin{align*}
D - 766 &= (-1)(d - 2) \
D &= -d + 768
\end{align*}

Therefore, the linear model for depth as a function of days is D = -d + 768, which matches choice C.

The Following Table Shows the Depth D , in Inches ddd

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