People enter a line for an escalator at a rate modeled by the function r given by 1. 440for O SI S 300 0 for 300, where r(t) is measured in people per second and t is measured in seconds. As people get on the escalator, they exit the line at a constant rate of 0.7 person per second. There are 20 people in line at time 0. (a) How many people enter the line for the escalator during the time interval 0 t S 300? (b) During the time interval 0 S I S 300, there are always people in line for the escalator. How many people are in line at time 300? (c) For> 300, what is the first time 1 that there are no people in line for the escalator? (d) For 0 sI s 300, at what time is the number of people in line a minimum? To the nearest whole number, find the number of people in line at this time. Justify your answer.