I do not know how to do question 1 and question 3? Can you explain what is P(t) stand for and how to do question 3?

1. The following equation gives a model for the spread of a rumor in a college town _ 1_ 1 + 048‘“ :c(t) Where 5:05) is the fraction of the students that knows the rumor at time t and a and k are positive con-stants. (a) Find the lim p(t)t—)oo(b) Find the rate of spread of the rumor (C) Graph cc for the case a = 12, k = 1/3 with t measured in hours. Use the graph to estimate how longit will take for 60% of the population to hear the rumor.