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1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: B(t) = 23, 000 – 80 sin () ants per day and the death rate is modelled by: D(t) = 21, 000 – 30 cos(37t) ants per day. (a) Compute 30 | (B(t) – D(t)) dt 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.

1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: B(t) = 23, 000 – 80 sin () ants per day and the death rate is modelled by: D(t) = 21, 000 – 30 cos(37t) ants per day. (a) Compute 30 | (B(t) – D(t)) dt 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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: nt B(t) = 23, 000 – 80 sin ants per day and the death rate is modelled by: D(t) = 21, 000 – 30 cos(37t) ants per day. (a) Compute 30 I (B(t) – D(t)) dt 15 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?
Transcribed Image Text:1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: nt B(t) = 23, 000 – 80 sin ants per day and the death rate is modelled by: D(t) = 21, 000 – 30 cos(37t) ants per day. (a) Compute 30 I (B(t) – D(t)) dt 15 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?
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