At 3 pm, when the box office opens, there are 75 people waiting in line to buy tickets for a new movie. The rate that the box office sells tickets and moves people out of the line is given by s(t) , measured in people per hour. While tickets are being sold, more people are arriving and joining the line at a rate given by L(t), also measured in people per hour. Match each of the integral expressions given in the table to the correct interpretation.
5 Integral Interpretation
75+∫ L(t)dt A. The number of people to whom tickets
5 3 have been sold between 3 pm and 5 pm
∫ S(t)dt B. The number of people standing in line at 5 pm
3 C. The total number of people who have stood in
75+∫ L(t)dt-∫ S(t)dt line beginning at 3 pm and ending at 5 pm
∫ L(t)dt D. The change in the number of people in the line
∫ L(t)dt--S(t)dt between pm and 5 pm
E. The number of people who have arrived to join
the line between 3 pm and 5 pm