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) = N₀e^rt

where N(t) is the population at time t, N_o is the initial population and r is the per capita growth rate. 

If r_A, r_B, r_C are the intrinsic growth rates of populations A, B, and C respectively, which of these statements is true? 

Concept:

Exponential population growth

\(N(t) = N_0 e^{rt} \)

Here, \( r\) represents the intrinsic growth rate. 

Explanation:

 \(N(t) = N_0 e^{rt}\)

where, \(N(t)\) is the population at time t, \(N_0\) 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 \(r_A > r_B > r_C\)

Population A has the highest growth rate  \(r_A \) because its curve rises the fastest.

Population B has a slower growth rate \(r_B \) than A but faster than C.

Population C has the slowest growth rate  \(r_C\) .

The correct answer is Option 4).