1.

Suppose that for a certain leafcutter ant colony, the birth rate is modelled by: t B(t) = 23, 000 805111 (7%) ants per day and the death rate is modelled by: D(t) = 21, 000 30 cos(37rt) ants per day. (a) Compute 30 5 (Bdt and briefly explain what this quantity represents in terms of the colony. (b) Compute the average number of ants born per day, in the time from t = 10 days to t = 40 days. (c) Suppose that at time t = 0, there are 739,000 ants in the colony. According to the model, how many ants are in the colony at time t = 31? 43 Let y = du. Use the Fundamental Theorem of Calculus to find y'. 1-5x 1 + u2-The velocity function (in meters per second) for a particle moving along a line is given by 110') = t3 51'2. Find the displacement and the distance traveled by the particle during the time interval [-1,7]. (Hint: Draw a graph of the velocity function.) Your answers require that you enter the correct units. Displacement = Distance traveled =