A rumor spreads through a small town. Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1 − y that has not yet heard the rumor. The differential equation satisfied by y in terms of a proportionality factor k is y'(t) = ky(1 − y), where k is a constant of proportionality. Find k (in units of days−1), assuming that 10% of the population knows the rumor at t = 0 and 40% knows it at t = 3 days. (Round your answer to two decimal places.) k = days−1