\fConsider a beehive of l bees. Suppoee that an outbreak of a virus oocure in the beehive. Once a bee becomes infected, the bee remains infected and does not recover. The virus does net kill the beers. Let Ht} 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]: [[t] satises the ODE {if {it ,3 { DU J where ,3 I} I] is a constant. Explain why, with referenee to the information given above. % (d) What happens to I(t) as t - co? Justify your answer. Interpret this in terms of the virus's spread through the beehive.(c) The outbreak begins with 100 infected bees at time t = 0. 3 days later there are 1000 infected bees. Find /(t) in terms of t