Question

the owner of a retail store is tracking his inventory for an annual report. the graph shows the remaining inventory for a particular item and the number of days that have passed since the stock was replenished.

which type of function best models the relationship between the number of days and the inventory remaining?

a. a quadratic function with a negative value of a
b. a linear function with a positive slope
c. a linear function with a negative slope
d. a square root function

Explanation:

1. Analyze the trend: As the number of days (x - value) increases, the inventory remaining (y - value) decreases.
2. Analyze the shape: The points appear to lie close to a straight line. A linear function has the form \(y = mx + b\), where \(m\) is the slope. Since \(y\) decreases as \(x\) increases, the slope \(m\) should be negative.
3. Eliminate other options:

• Option A: A quadratic function would have a parabolic shape (curved), but the points here are linear, so A is incorrect.
• Option B: A positive slope would mean \(y\) increases as \(x\) increases, which is the opposite of what we see, so B is incorrect.
• Option D: A square - root function has a curve that starts with a steep slope and then flattens, which does not match the linear trend here, so D is incorrect.

Answer:

C. a linear function with a negative slope