A hypothetical population has a carrying capacity of 1,500 individuals and r(max) is 1.0. The population growth rate is negative for a population with a size of 1,800 individuals. The population loses 360 individuals.
It is given that,
N = 1800, r = 1.0, K = 1500
where, N = Population density at time t
r = Intrinsic rate of natural increase
K = Carrying capacity
Now, the population growth rate can be calculated by using logistic growth rate equation as follows:-
dN/dt = rN ( (K-N)/K)
= 1.0 x 1800 ( (1500-1800)/1500)
= 1800 x (-300/1500)
= 1800 x (-1/5)
= -360
Thus, the growth rate is negative.
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