2. A store is having a 12-hour sale. The total number of shoppers who have entered the store t hours after the sale begins is modeled by the function S defined by S(t) = 0.51* - 16t + 144t for 0 S t S 12. At time t = 0, when the sale begins, there are no shoppers in the store. (a) At what rate are shoppers entering the store 3 hours after the start of the sale? Do not write beyond this border. (b) Find the value of ~ | S'(t) dt. Using correct units, explain the meaning of _ S'(t) di in the context of this problem.(c) The rate at which shoppers leave the store, measured in shoppers per hour, is modeled by the function L defined by L(t) = -80 + 4400 for 0