The population of a city is plotted against time (in years) in the graph…
2010
The population of a city is plotted against time (in years) in the graph below.
Which inference can be drawn from the graph?
Answer: D. The population initially increases exponentially and then stabilizes. — ConceptIn logistic population growth, the per-capita growth rate decreases as the population approaches the environment’s carrying capacity K. When the…
- A.
The population increases exponentially.
- B.
The population increases in a parabolic fashion.
- C.
The population initially increases linearly and then stabilizes.
- D.
The population initially increases exponentially and then stabilizes.
Show answer & explanation
Correct answer: D
Concept
In logistic population growth, the per-capita growth rate decreases as the population approaches the environment’s carrying capacity K.
When the population N is much smaller than K, growth is approximately exponential; as N approaches K, the net growth rate tends to zero, producing an S-shaped curve with a plateau.
Application
At the beginning, the plotted curve bends upward and becomes progressively steeper, which is the exponential phase.
Later, the slope decreases and the curve approaches the dashed horizontal limit, showing that growth slows as the carrying capacity is approached.
Near the upper limit, the curve becomes almost horizontal, so the population stabilizes instead of increasing without bound.
Contrast and cross-check
Pure exponential growth would keep becoming steeper and would not approach a horizontal plateau.
Parabolic growth would follow a quadratic trend and would not have this carrying-capacity asymptote.
Linear growth followed by stability would show a straight rising segment with constant slope before becoming flat, unlike the curved rising segment shown.
Exponential growth followed by stability gives the observed early acceleration and later plateau.
Therefore, the population initially increases exponentially and then stabilizes.