2022 AP Calculus AB FRQ #1

From 5 A.M. to 10 A.M., the rate at which vehicles arrive at a certain toll plaza is given by A(t), where t is the number of hours after 5 A.M. and A(t) is measured in vehicles per hour. Traffic is flowing smoothly at 5 A.M. with no vehicles waiting in line. (a) Write, but do not evaluate, an integral expression that gives the total number of vehicles that arrive at the toll plaza from 6 A.M. (t = 1) to 10 A.M. (t = 5). (b) Find the average value of the rate, in vehicles per hour, at which vehicles arrive at the toll plaza from 6 A.M. (t = 1) to 10 A.M. (t = 5). (c) Is the rate at which vehicles arrive at the toll plaza at 6 A.M. (t = 1) increasing or decreasing? Give a reason for your answer. (d) A line forms whenever A t( ) ≥ 400. The number of vehicles in line at time t is given by an expression, where a is the time when a line first begins to form. To the nearest whole number, find the greatest number of vehicles in line at the toll plaza in the time interval. Justify your answer. Timestamps Intro: 00:00 Part a: 00:29 Part b: 01:59 Part c: 03:58 Part d: 05:41