Consider the spreading of a rumor through a company of 1000 employees. The number of people hearing the rumor each day is proportional to the product of the number who have heard the rumor previously and the number who have not heard the rumor. This is given by
rn+1= rn + 1000krn(1000-rn)
k is a parameter that depends on how fast the rumor spreads and n is the number of days. Assume k = .001 and that 4 people initially heard the rumor.
How soon will all 1000 employees have heard the rumor?
So at day 0, or r1, r1 = ro+ 1000(.001)r0(1000-r0) or r1= 4 + 1 * 4 * 996 = 3988
My problem is that the k value doesn't do much. I mean 1000 * .001 is 1 so I feel that messes up the model. But this model was in the book and I tried modifying this model with: rn+1= rn + 1000krn -k*(rn)2 This model worked out better, but I still didn't get the answer that is in the back of the book.
The answer is that at day 8 973 people heard the rumor and day 9 1852 people heard the rumor. So the answer is in between days 8 and 9. I need help finding this correct answer.
rn+1= rn + 1000krn(1000-rn)
k is a parameter that depends on how fast the rumor spreads and n is the number of days. Assume k = .001 and that 4 people initially heard the rumor.
How soon will all 1000 employees have heard the rumor?
So at day 0, or r1, r1 = ro+ 1000(.001)r0(1000-r0) or r1= 4 + 1 * 4 * 996 = 3988
My problem is that the k value doesn't do much. I mean 1000 * .001 is 1 so I feel that messes up the model. But this model was in the book and I tried modifying this model with: rn+1= rn + 1000krn -k*(rn)2 This model worked out better, but I still didn't get the answer that is in the back of the book.
The answer is that at day 8 973 people heard the rumor and day 9 1852 people heard the rumor. So the answer is in between days 8 and 9. I need help finding this correct answer.