Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy dt NOTE: Round your answers to two decimal places. = (0.5+ sin t) 5 a) If y(0) = 1, find (or estimate) the time 7 at which the population has doubled. Choose other initial conditions and determine whether the doubling time 7 depends on the initial population. The doubling time is 7 = 3 X The doubling time does not depend on the initial population. 1 b) Suppose that the growth rate is replaced by its average value 10 Determine the doubling time in this case. In this case, T = 6.93 c) Suppose that the term sint 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, T = 6.8459 X Edit
Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy dt NOTE: Round your answers to two decimal places. = (0.5+ sin t) 5 a) If y(0) = 1, find (or estimate) the time 7 at which the population has doubled. Choose other initial conditions and determine whether the doubling time 7 depends on the initial population. The doubling time is 7 = 3 X The doubling time does not depend on the initial population. 1 b) Suppose that the growth rate is replaced by its average value 10 Determine the doubling time in this case. In this case, T = 6.93 c) Suppose that the term sint 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, T = 6.8459 X Edit
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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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
dt
NOTE: Round your answers to two decimal places.
=
(0.5+ sin t)
5
a) If y(0) = 1, find (or estimate) the time 7 at which the population
has doubled. Choose other initial conditions and determine whether
the doubling time r depends on the initial population.
The doubling time is 7 = 3
X
The doubling time does not
depend on the initial population.
1
b) Suppose that the growth rate is replaced by its average value 10
Determine the doubling time in this case.
In this case, T = 6.93
c) Suppose that the term sint 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, T = 6.8459
X
Edit
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