A student hears that her class midterm has been cancelled, believes it, and shares on a social media platform and a rumor starts. Students can be in three states: Haven't heard the rumor yet (II), convinced the rumor is true (T), and convinced the rumor is false (F). Students in the H category can be convinced to move to T or F when they contact students in those categories. Students in the T category can be convinced by those in F. Students in F never change their minds. a. Draw a diagram with these state variables. b. Write a system of differential equations for this scenario. Define all of the parameters you used, their units. c. What are the initial conditions? d. Using the fact that the total number of students is a constant N, find the phase plane and sketch a phase plane trajectory. Where does the population end up? a A student hears that her class midterm has been cancelled, believes it, and shares on a social media platform and a rumor starts. Students can be in three states: Haven't heard the rumor yet (II), convinced the rumor is true (T), and convinced the rumor is false (F). Students in the H category can be convinced to move to T or F when they contact students in those categories. Students in the T category can be convinced by those in F. Students in F never change their minds. a. Draw a diagram with these state variables. b. Write a system of differential equations for this scenario. Define all of the parameters you used, their units. c. What are the initial conditions? d. Using the fact that the total number of students is a constant N, find the phase plane and sketch a phase plane trajectory. Where does the population end up? a