Suppose that a rumor spreads according to a logistic model. At time t = 0, half

Question

Suppose that a rumor spreads according to a logistic model. At time t = 0, half of a population of 100,000 have heard this rumor, and at that time the number who’ve heard the rumor is increasing at 1000 people/day.
(a) Determine the number of people who have heard the rumor on day t > 0.
(b) Determine to the nearest whole day the length of time it will take for 80% of the population to have heard this rumor.

[Hint: Find a and b for the logistic model by solving a system of equations. One of the equations in your system comes from dP/dt=P(a-bP) and the other comes from the relationship of a and b to the carrying capacity.]

Explanation / Answer

(in thousands) P = 100 Po = 50 Rate = 1 = dP/dt t = 0 What is t when P(t) = 80% of P? dP/dt = kP(M-P) 1 = k*50(100-50), so k = .0004 Then, once you know k, P(t) = M*P / Po + (M-Po)exp(-k*M*t) So then with P(t) = 80, t = 34.6574 about 35 years

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.