Final answer:
Different functions have distinctive growth patterns. Linear growth is constant and creates a straight line graph, exponential growth's rate increases and has a steep curve, logarithmic growth slows over time, and quadratic growth is proportional to a square, resulting in a parabolic graph. Human population growth can be exponential at first and becomes logistic as resources diminish.
Step-by-step explanation:
Different functions exhibit different types of growth patterns. Linear growth is characterized by a constant increase or decrease, forming a straight line when graphed. Exponential growth is identified by the rate of growth increasing over time, often leading to a steep curve that represents rapid increase, especially as the amount grows larger. Logarithmic growth increases initially but then the rate of growth slows over time, resulting in a curve that levels off as it moves to the right. Lastly, quadratic growth includes any growth that is proportional to a square of some variable, typically resulting in a parabolic shape on a graph.
Considering the information provided and the growth models in question - exponential and logistic growth among natural populations - human population growth can often be described by one of these models. In the early phases, this growth may appear exponential, with the number of individuals doubling at regular intervals, illustrated by a J-shaped curve. However, as resources become limited, the growth rate decreases, and the population growth begins to level off; this is called logistic growth, which is shown by an S-shaped curve. Examples of exponential growth in populations include bacteria growing in enriched mediums. Meanwhile, logistic growth might be observed in human populations or animal populations as they near carrying capacity due to limited resources.