Precalculus & Modeling- Spring 2022 Name Test 2 - [46 Total Points] Part II - Calculator Required - 18 Points 6. [6 pts] A student brought a cold beverage to precalculus class, but she was so excited about what she was learning that she forgot all about it. As the beverage sat in the classroom it warmed up, and the temperature at time t could be modeled by the equation T(t) = - 35e-0.03t +72, where t is measured in minutes since the student entered the classroom and T is measured in degrees Fahrenheit. a) Sketch a graph of the function T(t). Be sure to label any intercepts and asymptotes. b) How long will it take until the temperature of the beverage is 60 degrees Fahrenheit? Show algebraic work to support your answer. 7. [6 pts] In science class, Terrell is modeling the path that a beetle is taking as it moves toward a source of heat. Terrell noticed that the beetle moved along a linear path at a constant speed. At time t=0 seconds, the beetle was at coordinates (4, 6). The beetle reached the heat source located at coordinates (16, 24) at time t = 8 seconds. Write a set of parametric equations to model the path of the beetle over time