5. A population N has intrinsic growth rate r > 0 and is harvested at constant rate h>0 so that dN dt =rN-h. Determine N as a function of t and its initial value No > 0. Show that there is a threshold value k such that if h k then the population is driven to extinction.

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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F2
5. A population N has intrinsic growth rate r > 0 and is harvested at constant
rate h>0 so that
93
dN
dt
=rN - h.
Determine N as a function of t and its initial value No > 0. Show that there
is a threshold value k such that if h <k then N grows without bound while
if h > k then the population is driven to extinction.
#3
80
F3
23
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Q
F4
25. Let n be a positive even integer and let H be a subgroup of Z of odd
tv
%
5
F5
<CO
6
C
1
F6
&
7
F7
*
8
DII
F8
F9
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0
F10
E RT Y UI O P
Transcribed Image Text:W F2 5. A population N has intrinsic growth rate r > 0 and is harvested at constant rate h>0 so that 93 dN dt =rN - h. Determine N as a function of t and its initial value No > 0. Show that there is a threshold value k such that if h <k then N grows without bound while if h > k then the population is driven to extinction. #3 80 F3 23 $ Q F4 25. Let n be a positive even integer and let H be a subgroup of Z of odd tv % 5 F5 <CO 6 C 1 F6 & 7 F7 * 8 DII F8 F9 ) 0 F10 E RT Y UI O P
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