Question 2. Consider a simple model for a population N(t) of marine invertebrates at time t, measured in days, where the per capita birth rate is proportional to the temper- ature of the ocean at time t, T(t), and the per capita death rate is proportional to the salinity of the ocean, S(t): dN dt dN dt 2πt On the west coast of BC, a simple model for ocean temperature in degrees Celsius is T(t) = 9-3 cos and a simple model for ocean salinity in parts per thousand (ppt) is S(t) = 25+7 cos (3), so the model becomes 365 = = (bT(t))N- (dS(t))N. b 9-3 cos 5 (⁹ (365)) N-d (25 N-d 25+ 7 cos 2πt 365 Find the population size N(t), with the initial condition N(0) = 100, (a) when b= 1/9 and d = 1/25, (b) when b= 4/9 and d = 1/25, and (c) when b= 1/9 and d = 4/25. N.
Question 2. Consider a simple model for a population N(t) of marine invertebrates at time t, measured in days, where the per capita birth rate is proportional to the temper- ature of the ocean at time t, T(t), and the per capita death rate is proportional to the salinity of the ocean, S(t): dN dt dN dt 2πt On the west coast of BC, a simple model for ocean temperature in degrees Celsius is T(t) = 9-3 cos and a simple model for ocean salinity in parts per thousand (ppt) is S(t) = 25+7 cos (3), so the model becomes 365 = = (bT(t))N- (dS(t))N. b 9-3 cos 5 (⁹ (365)) N-d (25 N-d 25+ 7 cos 2πt 365 Find the population size N(t), with the initial condition N(0) = 100, (a) when b= 1/9 and d = 1/25, (b) when b= 4/9 and d = 1/25, and (c) when b= 1/9 and d = 4/25. N.
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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Transcribed Image Text:Question 2. Consider a simple model for a population N(t) of marine invertebrates at
time t, measured in days, where the per capita birth rate is proportional to the temper-
ature of the ocean at time t, T(t), and the per capita death rate is proportional to the
salinity of the ocean, S(t):
dN
dt
2πt
On the west coast of BC, a simple model for ocean temperature in degrees Celsius is
T(t)= 9-3 cos and a simple model for ocean salinity in parts per thousand (ppt)
is S(t) = 25+ 7 cos (3), so the model becomes
365
365
=
dN
dt
b
= (bT(t))N- (dS(t))N.
3 cos
(365)) N-d (2
N-d 25+ 7 cos
2πt
365
Find the population size N(t), with the initial condition N(0) = 100,
(a) when b= 1/9 and d = 1/25,
(b) when b = 4/9 and d = 1/25, and
(c) when b= 1/9 and d = 4/25.
N.
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