MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
A city’s outdoor concert begins at noon. The air temperature (in °C) near the stage is modeled for 0≤t≤6 hours by A(t)=18+4sin(3πt), while the temperature inside an exhibition hall 50 meters away is modeled by B(t)=22−3cos(2πt).
(a) Use the models to calculate A(0) and B(0) and to calculate A(6) and B(6). Show work.
(b) Determine whether there must be a time t between noon and 6 p.m. when the two temperatures are equal. State the time interval over which you know equality must occur and justify your conclusion.
(c) Explain how your reasoning in part (b) would change, if at all, if the domain were extended to 0≤t≤10. No calculation of additional values is necessary.