Question

A textile mill has a stock of 350 bags in their workshop. Their machines produce bags at a rate of 50 bags per hour. The production manager creates a graph to show the production of bags over time. If x is the number of hours the machines work and f(x) is the total number of bags produced, which of the following statements describes the end behavior of the graph?

a) As x increases,f(x) increases indefinitely.
b) As x increases, f(x) approaches a maximum value.
c) As x increases,f(x) remains constant.
d) As x increases, f(x) decreases indefinitely.

Answer 1

The end behavior of the graph showing the production of bags over time at a constant rate is that, as the number of hours increases, the total number of bags produced also increases indefinitely.

Step-by-step explanation:

The question involves understanding the end behavior of a graph that represents the production of bags over time. Given the context that the machines produce bags at a rate of 50 bags per hour and there is no mention of a maximum production limit, the graph representing the total number of bags produced over time will be a linear function. Therefore, the end behavior of the graph will be:

a) As x increases, f(x) increases indefinitely.

This is because for each additional hour of machine work, 50 more bags are produced, and this rate of production can, in theory, continue indefinitely without any specified constraints.