Suppose that a community contains 15,000 people who are susceptible to Michaud’s syndrome, a contagious disease. At time t = 0 the number N(t) of people who have developed Michaud’s syndrome is 5000 and is increasing at the rate of 500 per day. Assume that N'(t) is proportional to the product of the numbers of those who have caught the disease and of those who have not. How long will it take for another 5000 people to develop Michaud’s syndrome?