In a university of 30,000 students, the administration holds meetings to discuss the idea of bringing in a major rock band for homecoming weekend. Before the plans are officially announced, the 20 student representatives on the administrative council spread information about the event as a rumor. At the end of one week, 100 people know the rumor. Assuming logistic growth, how many people know the rumor after four weeks?

grabrovi0u

grabrovi0u

Answered question

2022-10-30

In a university of 30,000 students, the administration holds meetings to discuss the idea of bringing in a major rock band for homecoming weekend. Before the plans are officially announced, the 20 student representatives on the administrative council spread information about the event as a rumor. At the end of one week, 100 people know the rumor. Assuming logistic growth, how many people know the rumor after four weeks?

Answer & Explanation

latatuy

latatuy

Beginner2022-10-31Added 12 answers

Solution: let the logistic growth model
is f ( t ) = q 1 + b e c t ,   c < 0 lim f ( t ) = 9 = 30000 t = 0 f ( 0 ) = a 1 + b = 20 30000 1 + b = 20 1 + b = 1500 b = 1499 so  t = 1 week  f ( 1 ) = a 1 + b e c = 100 e c = ( 299 1499 ) c = ln ( 299 1499 ) = 1.6121 f ( t ) = 8894.31 f ( t ) 8900

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