Question

number of pencils sold over time:
a school store sells pencils. at the beginning of the year, they sell a lot of pencils, then sales drop, and finally, pencils are sold at a steady rate.
sketch a qualitative graph to represent the scenario.
(graph axes: number of pencils sold (x - axis), time (y - axis))

Explanation:

Step1: Analyze the sales phases

The sales of pencils have three phases: high initial sales, a drop, and then steady sales. We need to represent this on a graph with time on the y - axis (downward direction as per the given axis) and number of pencils sold on the x - axis.

Step2: Sketch the first phase (high initial sales)

In the first phase, a lot of pencils are sold. So, we start at a point on the graph (let's say at time \(t = 0\)) and draw a line with a relatively steep positive slope (since a lot of pencils are sold in a short time, the number of pencils sold increases rapidly with respect to time).

Step3: Sketch the second phase (sales drop)

In the second phase, sales drop. So, from the end - point of the first phase, we draw a line with a negative slope (the number of pencils sold decreases as time increases). The slope should be such that it represents a drop in sales.

Step4: Sketch the third phase (steady rate)

In the third phase, pencils are sold at a steady rate. So, from the end - point of the second phase, we draw a line with a constant (positive) slope (since pencils are still being sold, the number of pencils sold increases with time at a steady rate, so the slope is positive and constant).

(Note: Since it's a qualitative sketch, we focus on the general shape. The x - axis is "Number of Pencils Sold" and y - axis is "Time" (with time increasing downward). So, a steeper line in the first phase (more pencils sold in less time), a line going downward (sales drop, so as time increases (moving down the y - axis), the number of pencils sold (x - axis) decreases) in the second phase, and a line with a constant slope (steady sales, so as time increases, the number of pencils sold increases at a constant rate) in the third phase.)

Answer:

The qualitative graph will have three segments:

1. A steeply increasing segment (high initial sales).
2. A decreasing segment (sales drop).
3. A linearly increasing segment with a constant slope (steady sales rate).

(To visualize, on the given axes: start at a point, go right - up steeply (first phase), then right - down (second phase), then right - up with a constant slope (third phase), where the y - axis (time) increases downward and x - axis is number of pencils sold.)