Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy (0.4 + sin t) dt || 4 NOTE: Round your answers to two decimal places. a) If y(0) 1, find (or estimate) the time T at which the population || has doubled. Choose other initial conditions and determine whether the doubling time ↑ depends on the initial population. The doubling time is 7 = The doubling time Choos depend on the initial population one ▼ 1 b) Suppose that the growth rate is replaced by its average value 10 Determine the doubling time t in this case.
Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy (0.4 + sin t) dt || 4 NOTE: Round your answers to two decimal places. a) If y(0) 1, find (or estimate) the time T at which the population || has doubled. Choose other initial conditions and determine whether the doubling time ↑ depends on the initial population. The doubling time is 7 = The doubling time Choos depend on the initial population one ▼ 1 b) Suppose that the growth rate is replaced by its average value 10 Determine the doubling time t in this case.
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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Question
Need answers for a, b & c
![Suppose that a certain population has a growth rate that varies with
time and that this population satisfies the differential equation
dy
(0.4 + sin t)
dt
4
NOTE: Round your answers to two decimal places.
a) If y(0) = 1, find (or estimate) the time T at which the population
has doubled. Choose other initial conditions and determine whether
the doubling time t depends on the initial population.
The doubling time is T =
The doubling time Choose one
depend on the initial population.
1
b) Suppose that the growth rate is replaced by its average value
10
Determine the doubling time T in this case.
In this case, ↑ =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc373888-a70a-4c0e-9c9b-f21d80fbbf5a%2F31fe746f-cc1f-4838-89b1-034191a7dda8%2F0pjmdgk_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that a certain population has a growth rate that varies with
time and that this population satisfies the differential equation
dy
(0.4 + sin t)
dt
4
NOTE: Round your answers to two decimal places.
a) If y(0) = 1, find (or estimate) the time T at which the population
has doubled. Choose other initial conditions and determine whether
the doubling time t depends on the initial population.
The doubling time is T =
The doubling time Choose one
depend on the initial population.
1
b) Suppose that the growth rate is replaced by its average value
10
Determine the doubling time T in this case.
In this case, ↑ =
![c) Suppose that the term sin t in the differential equation is replaced
by sin(2nt); that is, the variation in the growth rate has a
substantially higher frequency. What effect does this have on the
doubling time T ?
In this case, ↑ =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc373888-a70a-4c0e-9c9b-f21d80fbbf5a%2F31fe746f-cc1f-4838-89b1-034191a7dda8%2Fbqs4cwj_processed.png&w=3840&q=75)
Transcribed Image Text:c) Suppose that the term sin t in the differential equation is replaced
by sin(2nt); that is, the variation in the growth rate has a
substantially higher frequency. What effect does this have on the
doubling time T ?
In this case, ↑ =
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