Question
Asked Oct 23, 2019
63. Logistic Growth A population of organisms grows according
to a logistic growth model:
K
N(t)=
1+ (K-1) e-mt
where r and K are positive constants.
0I:A
visvi90
(a) Find dN.
ST
(b) Show that N(t) satisfies the equation
1-)
N
rN 1
K
utoimiiol Strisdr HeaN
gol od to ovissvisb et
help_outline

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63. Logistic Growth A population of organisms grows according to a logistic growth model: K N(t)= 1+ (K-1) e-mt where r and K are positive constants. 0I:A visvi90 (a) Find dN. ST (b) Show that N(t) satisfies the equation 1-) N rN 1 K utoimiiol Strisdr HeaN gol od to ovissvisb et

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check_circleExpert Solution
Step 1

A population of organisms grow according to a logistic growth model

К
N(t)=
1+(K-1)e
a) Find Dn Dt
b) Show that n(t) satisfies the equation
N
= rN 1-
К
dt
help_outline

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К N(t)= 1+(K-1)e a) Find Dn Dt b) Show that n(t) satisfies the equation N = rN 1- К dt

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Step 2

Find the first order deriva...

K
N(t)
1+(K -1)e
dN
-K
K
x0+
N(0)
-re"
dt
K
-rt
1+
K
-1 re"
N(0)
1K
K
1K
help_outline

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K N(t) 1+(K -1)e dN -K K x0+ N(0) -re" dt K -rt 1+ K -1 re" N(0) 1K K 1K

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