The yearbook club has 5 members returning from last year. They set up a booth in the cafeteria to recruit more members, and an average of 3 new members sign up each day. Which **best** describes why the graph relating the total number of members on the yearbook club, *m*, and the number of days the booth is set up, *d*, will be continuous or discrete?

The graph will be continuous because an end day for the booth being set up is not given in the description.

The graph will be continuous because there can be any number of people signing up each day since we are only given the average.

The graph will be discrete because some day the number of available people to sign up for the club will run out.

The graph will be discrete because there is no such thing as a partial person to sign up and the booth is set up once each day for sign ups.

To determine whether the graph relating the total number of members on the yearbook club (\(m\)) and the number of days the booth is set up (\(d\)) is continuous or discrete, we need to consider the nature of the variables involved.

In this scenario:
- \(d\) represents the number of days the booth is set up.
- \(m\) represents the total number of members.

Given:
- There are 5 members initially.
- An average of 3 new members sign up each day.

The key considerations are:
1. The number of days (\(d\)) is a countable value and can only be whole numbers (0, 1, 2, 3, ...).
2. The number of new members each day is also a countable value and must be a whole number, meaning that you can't have a fraction of a person signing up.

Therefore, the relationship between the total number of members (\(m\)) and the number of days (\(d\)) will involve only whole numbers. This means the graph will consist of distinct points rather than a continuous curve.

Given this reasoning, the correct description is:

**The graph will be discrete because there is no such thing as a partial person to sign up and the booth is set up once each day for sign ups.**

Would you like more details or have any questions?

Here are 5 questions you might want to ask:
1. How can you represent this situation with an equation relating \(m\) and \(d\)?
2. What is the difference between continuous and discrete data in graphing?
3. Can you explain more about types of graphs used for discrete and continuous data?
4. How would the graph look like if the number of sign-ups varied each day?
5. What are some real-life examples of continuous and discrete data?

**Tip:** When deciding if a graph is continuous or discrete, think about whether the data can take on any value within a range (continuous) or only specific, distinct values (discrete).

Explore why the graph of total yearbook club members over days is discrete, considering the average daily sign-ups and initial members. This problem covers key concepts in graphing and data types. Suitable for students in Grades 6-8.

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