Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy (0.5+sin(t))y 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 7?
Suppose that a certain population has a growth rate that varies with time and that this population satisfies the differential equation dy (0.5+sin(t))y 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 7?
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
(0.5+sin(t))y
5
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?
O The doubling time gets smaller. Since the growth rate has a higher frequency, the population would
get faster to double the original size.
O The doubling time changes and gets almost three times as the original one. Since the growth rate
changes so fast, the population changes from growth to decay too fast to have a significant
growth.
O The doubling time changes and get bigger. Since the frequency is bigger, the equation becomes
non-linear, which makes the solution to grow slower than the original.
O The doubling time is almost three times smaller. Since the frequency is higher, the growth would
be faster and the doubling time would be smaller.
O The doubling time remains almost the same. Since the average growth is the same, the doubling
time would remain almost the same.
O The doubling time remains the same. A higher frequency in the rate of growth does not affect the
doubling time since the function is periodic.
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