Exercise IV [20 points] - To Upload on Gradescope The rumor that Ralph will give everybody an A in this class spreads through our class. Suppose there are 21ml students in this class. Let 1' he the number of students who heard the rumor. r's rate of spread is proportional to the number of students who have not heard it. If t is time in hours1 we get: dr E = Gdi} - r}, 1. Is the function t] = Elle2* a solution to this differential equation? 'Why or why not? 2. Assuming that 10 students initiated the rumor [t = lUr}: {a} Solve the differential equation. (h) How long will it take for half the class to hear the rumor? Leave the nal answer exact