Question

representing relationships
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 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.

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

Explanation:

To determine if the graph is discrete or continuous, we analyze the nature of the variables. The number of members \( m \) and days \( d \) relate to counting people (members) and days. A discrete graph consists of distinct, separate points because you can't have a fraction of a person or a fraction of a day in this context (you can't have 0.5 of a member signing up, and the booth is set up per day, so days are whole numbers).

• The first option explains that since you can't have a partial person signing up and the booth is set up once per day (so days are whole - number intervals), the graph is discrete.
• The second option is wrong because even with an average, the number of members signing up must be a whole number (you can't have a fraction of a person), so it can't be continuous.
• The third option is wrong because the reason for being discrete is not about people running out, but about the nature of counting people (whole numbers).
• The fourth option is wrong because the absence of an end day doesn't make it continuous; the key is the nature of the variable (number of members is a count of people, which is discrete).

Answer:

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.