Math Problem Statement

What do I do

When a new laptop became available in a store, the number sold in the first week was high. Sales decreased over the next two weeks and then they remained steady over the next two weeks. The following week, the total number sold by the store increased slightly. Sketch the graph that represents this function over the six weeks.

Solution

This question asks you to sketch a graph based on a given scenario describing how sales change over time. Here's how to interpret and draw the graph:

Steps to Sketch the Graph:

  1. Start by labeling the axes:

    • The x-axis represents "Weeks" (1 to 6).
    • The y-axis represents "Sales."
  2. Interpret the scenario:

    • Week 1: Sales are high.
    • Weeks 2-3: Sales decrease.
    • Weeks 4-5: Sales remain steady.
    • Week 6: Sales increase slightly.
  3. Plot the behavior:

    • Begin at a high point on the y-axis for week 1.
    • Draw a downward slope from weeks 2 to 3 to show decreasing sales.
    • Draw a horizontal line from weeks 4 to 5 to indicate steady sales.
    • Finish with a slight upward slope for week 6 to represent the slight increase.
  4. Smooth the transitions:

    • Make the graph continuous by avoiding sharp corners between weeks.

Would you like me to sketch this for you? Let me know if you'd like a detailed explanation of any part!


Related Questions:

  1. How would the graph change if sales increased in week 4 instead of staying steady?
  2. Can you describe how to find the slope during weeks 2–3?
  3. What real-world factors might cause sales to decrease initially?
  4. How would the graph look if sales dropped to zero in week 5?
  5. How could this problem be expressed as a piecewise function?

Tip:

Always use consistent labels and scales on your axes to make your graph clear and easy to interpret.

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Math Problem Analysis

Mathematical Concepts

Graphing
Linear and Non-linear Functions
Piecewise Functions

Formulas

Linear graph functions (y = mx + b)

Theorems

Understanding and interpreting sales data in graph form

Suitable Grade Level

Grades 6-9