1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: B(t) nt = 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 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 time t = 0, there are 739,000 ants in the colony. According to the model, how many ants are in the colony at timet = 31?

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:
at
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
r30
I (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?
Transcribed Image Text:1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: at 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 r30 I (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?
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