Consider a beehive of 100,000 bees. Suppose that an outbreak of a virus occurs in the beehive. Once a bee becomes infected, the bee remains infected and does not recover. The virus does not kill the bees. Let I(t) be the number (in thousands) of bees that are infected at time t days after the start of the outbreak. The rate of increase of I at time t is proportional to the product of the number of bees which are infected at time t, and the number of bees which are not infected at time t. (a) I(t) satisfies the ODE dI dt. = BI(100-I)
Consider a beehive of 100,000 bees. Suppose that an outbreak of a virus occurs in the beehive. Once a bee becomes infected, the bee remains infected and does not recover. The virus does not kill the bees. Let I(t) be the number (in thousands) of bees that are infected at time t days after the start of the outbreak. The rate of increase of I at time t is proportional to the product of the number of bees which are infected at time t, and the number of bees which are not infected at time t. (a) I(t) satisfies the ODE dI dt. = BI(100-I)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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(b) Find the general solution of the ODE.
(c) The outbreak begins with 100 infected bees at time t = 0. 3 days later there are 1000
infected bees. Find I(t) in terms of t.
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