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)

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