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) / 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 T = The doubling time Choose one depend on the initial population... b) Suppose that the growth rate is replaced by its average value Determine the doubling time in this case. In this case, T= 1 10 c) Suppose that the term sint in the differential equation is replaced by sin(2πt); that is, the variation in the growth rate has a substantially higher frequency. What effect does this have on the doubling time 7 ? T In this case, T =
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) / 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 T = The doubling time Choose one depend on the initial population... b) Suppose that the growth rate is replaced by its average value Determine the doubling time in this case. In this case, T= 1 10 c) Suppose that the term sint in the differential equation is replaced by sin(2πt); that is, the variation in the growth rate has a substantially higher frequency. What effect does this have on the doubling time 7 ? T In this case, T =
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+ sint) /
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 =
The doubling time Choose one depend on the initial population.
b) Suppose that the growth rate is replaced by its average value
Determine the doubling time 7 in this case.
In this case, T=
1
10
c) Suppose that the term sint in the differential equation is replaced
by sin(2πt); 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 =
Transcribed Image Text:Choose one
Choose one
does
does not
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