1. People enter a line for an escalator at a rate modeled by the function r given by ⎧ 37tt⎪⎪⎪44 1 for 0 ££t ⎪()(− ) 300rt()=⎨ 100 300⎪⎪0 for t>300,⎪⎪ ⎩ where rt()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 t=0. (a) How many people enter the line for the escalator during the time interval 0 t 300 ££?(b) During the time interval 0 t 300££, there are always people in line for the escalator. How many peopleare in line at time t=300 ? (c) For t>300, what is the first time t that there are no people in line for the escalator? (d) For 0 t 300££, at what time t is the number of people in line a minimum? To the nearest wholenumber, find the number of people in line at this time. Justify your answer.