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Chapter 6: Problem 16

Sketch a graph that represents the scenario described in the exercise. Be sure to clearly label any variables and the coordinate axes. Keep in mind that various graphs may be drawn to represent each situation. The price of a certain stock starts the day at \(\$ 15\) per share. Over the first 2 hours of trading, the price of the stock steadily declines to \(\$ 13\) per share. It remains at that price for 3 hours and then declines to \(\$ 11.50\) per share over the next hour.

Short Answer

Expert verified
Graph starts at (0,15), declines to (2,13), stays steady until (5,13), then declines to (6,11.5).

Step by step solution

01

Set Up the Axes

On graph paper or using graphing software, draw the x-axis (time in hours) and the y-axis (price in dollars). Label the x-axis with 'Time (hours)' and the y-axis with 'Price (dollars)'.
02

Plot the Starting Point

Plot the initial point where the price of the stock is \( \$15 \) at time \( 0 \) hours.
03

Represent the First Decline

Since the stock price declines from \ \$15 \ to \( \$13 \) over the first 2 hours, draw a straight line from the point (0, 15) to the point (2, 13).
04

Represent the Stable Period

Next, the price remains at \( \$13 \) for 3 hours. Draw a horizontal line from (2, 13) to the point (5, 13).
05

Plot the Final Decline

Finally, the stock price drops to \( \$11.50 \) over the next hour. Draw a straight line from the point (5, 13) to the point (6, 11.5).
06

Label the Graph

Label the significant points on your graph. These points are (0, 15), (2, 13), (5, 13), and (6, 11.5). Also, add a title to your graph such as 'Stock Price Over Time'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

coordinate axes
To start graphing stock prices, understanding the coordinate axes is key.
Coordinate axes help us visually represent data on a graph.
The x-axis typically represents time, and the y-axis represents the variable being measured, like stock prices.
Drawing the axes correctly and labeling them clearly will set a strong foundation for your graph.

When preparing your graph:
  • Draw a horizontal line for the x-axis to represent time in hours.
  • Draw a vertical line for the y-axis to represent the price in dollars.
  • At the intersection of these two lines, you will have the origin point (0,0).

Once your axes are set up, label them.
For example, 'Time (hours)' on the x-axis and 'Price (dollars)' on the y-axis.
This helps readers instantly know what the graph is about.

Proper coordinate axes make your graph easier to read and understand.
plotting points
Plotting points is a fundamental step in graphing stock prices.
Points represent significant values or changes in the data set.
Each point on your graph has coordinates formatted as (x,y), where x is the time and y is the stock price.

To plot points:
  • Identify the important values from the problem.
  • In your case, these are the times and corresponding stock prices.
  • For example, plot (0, 15) to show the starting stock price of \(15 at 0 hours.

Continue plotting each significant point:
  • (2, 13) for when the stock price drops to \)13 after 2 hours

Connecting these points appropriately鈥攅ither with a line or curve鈥攈elps illustrate changes over time.
Ensure each point is accurately placed to maintain the graph鈥檚 integrity.
labeling graphs
Labeling your graph is crucial for clear communication.
Labels can make or break the readability of your graph, so don't skimp on this step!

There are two main types of labels on a graph:
  • Axis labels
  • Data point labels

Begin with axis labels.
As previously mentioned, label the x-axis as 'Time (hours)' and the y-axis as 'Price (dollars)'.
Next, label key data points to highlight pivotal changes.
In your case, label points like (0, 15), (2, 13), (5, 13), and (6, 11.5).

Additionally, adding a title such as 'Stock Price Over Time' synthesizes what the graph represents.

A thoroughly labeled graph is not only more professional but also significantly aids in understanding the data.

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Most popular questions from this chapter

The Metropolitan Transportation Authority charges \(\$ 1.75\) per ride on public transportation. They offer a monthly commuter pass for \(\$ 48\) that allows unlimited travel on the public transportation system. Let \(n\) represent the number of trips taken per month on public transportation and \(C\) represent the cost of all these trips. (A) Write an equation for the transportation cost \(C\) if you buy the monthly pass and if you pay for each trip individually. (B) Sketch the graphs of the two equations obtained in part (a). Label the horizontal axis \(n\) and the vertical axis \(C\). (C) Using the graphs obtained in part (b), determine how many trips per month make it more economical to buy a monthly pass rather than pay per trip.

Cellmate Communications offers two monthly cellular phone plans. The Standard plan costs \(\$ 15\) per month plus \(\$ 0.22\) per minute of air time. The Deluxe plan costs \(\$ 35\) per month plus \(\$ 0.14\) per minute of air time. (A) Write an equation for the monthly cost \(C\) of the Standard plan and the Deluxe plan for a month in which you use \(m\) minutes. (B) Sketch the graphs of the two equations obtained in part (a). Label the horizontal axis \(m\) and the vertical axis \(C\). (C) Using the graphs obtained in part (b), determine how many air time minutes per month make it more economical to buy the Standard plan.

Solve each of the following verbal problems algebraically. You may use either a one or a two-variable approach. Two cars start at the same place and time, and travel in opposite directions. One car is traveling 15 kph faster than the other. After 5 hours the two cars are \(275 \mathrm{km}\) apart. Find the speed of each car.

An orchestral society put on a concert. The members sold 200 tickets in advance and 75 tickets at the door. They charged \(\$ 1.50\) more for tickets at the door than for advance-purchase tickets. If they collected a total of \(\$ 1075,\) how much did they charge for tickets at the door?

Solve each of the following verbal problems algebraically. You may use either a one or a two-variable approach. Pat and Carlos both belong to the same book club. Pat orders two regular selections and three specially discounted ones for a total of \(\$ 56.90 .\) Carlos orders three regular selections and four specially discounted ones for a total of \(\$ 80.85\) What are the prices of a regular and a specially discounted selection?
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