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The graph shows the growth curves for three independent populations (A, B, and C). The growth model for each of these populations is  N(t) = N0
Question

The graph shows the growth curves for three independent populations (A, B, and C). The growth model for each of these populations is 
N(t) = N0ert
where N(t) is the population at time t, No is the initial population and r is the per capita growth rate. 

If rA, rB, rC  are the intrinsic growth rates of populations A, B, and C respectively, which of these statements is true? 

A.

rA= rB= rC

B.

rA > rB= rC

C.

rA = rB> rC 

D.

rA> rB> rC

Correct option is D

Concept:
Exponential population growth

N(t) = N0ert

Here, r represents the intrinsic growth rate. 
Solution:
 N(t) = N0ert
where, N(t) is the population at time t, N0 is the initial population, and r is the intrinsic growth rate.
Population A grows the fastest, showing a steep increase.
Population B grows more moderately, with a gentler curve compared to A.
Population C grows the slowest, with the flattest curve among the three.
Since the growth rate r dictates the steepness of the exponential curve, the following relationship can be
inferred based on the graph rA > rB > rc
Population A has the highest growth rate  rA because its curve rises the fastest.
Population B has a slower growth rate rB than A but faster than C.
Population C has the slowest growth rate  rc.
The correct answer is Option ( d).

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