A simpler model for the spread of a rumor assumes that the rate at which the rumor spreads is proportional (with factor k) to the fraction of the population that has not yet heard the rumor.
(a) Compute the solutions to this model and the model of Exercise 8 with the values k = 0.9 and y₀ = 0.1.
(b) Graph the two solutions on the same axis.
(c) Which model seems more realistic? Why?