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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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