Question 1. (15 points) Let p(t) = - 8 tet > Depending on certain conditions, a rumor spreads according to the function p(t) such that p is the portion of the population that heard the rumor at time t (hours). Note that a portion of 50%, for example, would correspond to p = 0.5. (a) What is the function governing the rate of spread of the rumor? t -+ (b) Determine lim p(t) and lim p' (t). Explain the meaning of the results. (c) Compute how long it would take for 60 percent of the population to hear a rumor