Tracking the Dow The Dow Jones Industrial Averages at the...

Tracking the Dow The Dow Jones Industrial Averages at the close of trade on three consecutive days were as follows: $$\begin{array}{|c|c|c|c|} \hline \text { Day } & \text { Monday } & \text { Tuesday } & \text { Wednesday } \\ \hline \text { Close } & 12,981 & 12,964 & 12,947 \\ \hline \end{array}$$ Let $d$ represent the day, with $d=0$ corresponding to Monday, and let D represent the Dow Jones average. Plot the points $(d, D),$ and draw the graph. Explain the meaning of $\frac{\Delta \bar{D}}{\Delta d}$ (Graph can't copy)

Tracking the Dow The Dow Jones Industrial Averages at the close of trade on three consecutive days were as follows:
$$\begin{array}{|c|c|c|c|} \hline \text { Day } & \text { Monday } & \text { Tuesday } & \text { Wednesday } \\ \hline \text { Close } & 12,981 & 12,964 & 12,947 \\ \hline \end{array}$$
Let $d$ represent the day, with $d=0$ corresponding to Monday, and let D represent the Dow Jones average. Plot the points $(d, D),$ and draw the graph. Explain the meaning of $\frac{\Delta \bar{D}}{\Delta d}$
(Graph can't copy)

Key Concepts

Cartesian Coordinate System

This concept involves using a grid to represent ordered pairs of numbers, where one axis (typically the horizontal axis) represents the independent variable (in this case, the day), and the other axis (the vertical axis) represents the dependent variable (here, the Dow Jones average). Plotted points on this grid visually illustrate the relationship between these two variables and allow for analysis of trends or patterns over time.

Delta Notation (?)

Delta (?) is used to denote change in a quantity. In the expression ?D, it represents the change in the Dow Jones average, while ?d represents the change in the day count. This notation is crucial in measuring how one variable differs from one value to another, providing a basis for understanding change over time or across different conditions.

Rate of Change

The rate of change, represented by the ratio ?D/?d, quantifies how much the Dow Jones average changes with each unit change in the day variable. It is a measure of the average change per day and is fundamental in assessing trends or predicting future values assuming a consistent trend.

Slope of a Line

In the context of a graph, the quotient ?D/?d is analogous to the slope of the line connecting two or more points. The slope provides a measure of the steepness and direction of the line, indicating whether the Dow Jones average is increasing, decreasing, or remaining constant over the time period considered.

Transcript

00:01 In this problem, we're looking at the rate of change of a dow jones average closing cost at the end of a few days period.

00:09 We're kind of told to do a few things.

00:12 The first thing they give us some information, they give us our table, and they tell us that on the graph, d, which is on our x axis, is going to represent, or a lowercase day is going to represent our days, and that monday is going to actually represent day zero.

00:30 So for monday, this will be day zero.

00:33 Tuesday will be day one.

00:35 Wednesday will be day two.

00:39 The capital d is the dow jones average closing cost.

00:44 So for monday, it would be $12 ,981, tuesdays, and wednesday's amount.

00:51 So we're going to graph these three points.

00:53 And the dow jones average is where we're actually going to graph that on the y axis.

00:59 And then we're going to talk about the slope and what the slope means.

01:02 So let's start by graphing.

01:05 So for the monday, it is 12 ,981.

01:13 So it's about right there.

01:17 For day one or tuesday, it's 12 ,964.