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1. Şuppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: nt B(t) = 23,000 – 80 sin () %3D ants per day and the death rate is modelled by: D(t) = 21,000 - 30 cos(3nt) 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. (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?

1. Şuppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: nt B(t) = 23,000 – 80 sin () %3D ants per day and the death rate is modelled by: D(t) = 21,000 - 30 cos(3nt) 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. (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?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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(3nt) ants per day. (a) Compute r30 (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. (c) Suppose that at timet= 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: B(t) = 23,000 – 80 sin ants per day and the death rate is modelled by: D(t) = 21,000 – 30 cos(3nt) ants per day. (a) Compute r30 (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. (c) Suppose that at timet= 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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