
The right-hand side of Equation 1.53 with P(50Dt) replaced by P
A
(50) becomes
cP(nDt)[P
m
P(n Dt)] ¼ cP
A
(50)[P
m
P
A
(50)]
¼ 1:25 10
9
(9:7778 10
6
)[25 10
6
9:7778 10
6
]
¼ 0:1860 10
6
people=year (1:55)
in close agreement with the estimate of (d=dt)P(t)j
t¼50Dt
.
Further scrutiny of the logistic growth model, Equation 1.43, reveals several important and
noteworthy characteristics of the underlying population dynamics. Expressing the model in a
slightly different form
g(P) ¼
1
p
dP
dt
¼ c(P
m
P)(1:56)
where g(P), the rate of change in popula tion dP=dt divided by the population P, is called the
population growth rate. Different population models are normally ...