In the accompanying figure, which of the lines represents the highest per capita rate increase (r)?

Question

BlackTom AI · Accepted Answer

Let’s examine what the graph communicates about per capita growth rate r. In population growth plots, the per capita growth rate is reflected by how rapidly the population increases for a given number of generations; steeper curves indicate higher r.
Option a: Line A is the steepest curve among A, B, C, and D. Its population size rises fastest with each generation, which indicates the largest per capita growth rate r.
Option b: Line D is the flattest of the four curves, showing the slowest increase across generations. This implies the smallest or a relatively low r.
Option c: Line B is steeper than D but clearly less steep than A. It represents a higher r than D but not as high as A, so it does not have the maximum rate.
Option d: Line C lies between B and D in steepness. While it demonstrates a moderate growth rate, it does not surpass Line A in r.
To compare per capita rates, focus on the slope of each curve at any given generation: a steeper slope corresponds to a higher r. Line A’s trajectory demonstrates the greatest slope, especially noticeable as generations progress toward 7–8 where the gap between A and the others widens notably.
Therefore, the line with the highest per capita rate increase r is the one with the steepest ascent, which is Line A.

In the accompanying figure, which of the lines represents the highest per capita rate increase (r)?单项选择题

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