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?

Question

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.

Answer 1

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.

In this context, the total number of members on the yearbook club \( m \) and the number of days the booth is set up \( d \) form a relationship where new members can only be counted as whole individuals. Additionally, the booth operates on a daily basis, meaning each day can be treated as a distinct point in time without intermediate values. Thus, the changes in \( m \) will occur in discrete steps, corresponding to the whole number of members signing up per day.