Final Answer:
The coefficient ‘c’ in the function p(x) = ax2 + bx + c represents the initial number of people waiting in line, thus the correct option is b.
Step-by-step explanation:
The given function p(x) = ax2 + bx + c models the number of people waiting in line to enter an auditorium for a musical production. The coefficients ‘a’, ‘b’ and ‘c’ represent different factors that determine the number of people in the queue. The coefficient ‘a’ represents the rate of change of people entering the auditorium, i.e. the rate at which the number of people in the queue increases or decreases. The coefficient ‘b’ represents the time taken for the last person to enter, i.e. the amount of time it takes for the last person in the queue to enter the auditorium. Finally, the coefficient ‘c’ represents the initial number of people waiting in line.
In order to calculate the number of people waiting in line, we can use the function p(x) = ax2 + bx + c. In this equation, ‘x’ represents the number of time units that have passed since the queue began to form. For example, if the queue started forming at 10:00 am, then the number of people in the queue at 10:15 am would be p(15). The coefficient ‘c’ in the equation would represent the number of people in the queue at 10:00 am. In other words, it represents the initial number of people waiting in line.
To summarize, the coefficient ‘c’ in the function p(x) = ax2 + bx + c represents the initial number of people waiting in line. It is the initial number of people in the queue at the start of the queue formation.