Final answer:
The statement that the formula for exponential growth and decay is simply Y=C is false. A more accurate formula includes parameters for initial amount, growth rate, and time, typically represented as Y=Ce^(kt). Exponential growth is characterized by a rapidly increasing rate, while logistic growth accounts for environmental limits and stabilizes at the carrying capacity. Option B is the correct answer.
Step-by-step explanation:
The formula for exponential growth and decay is indeed not given simply by Y=C. The statement in the question is false. Exponential growth and decay refer to processes where quantities increase or decrease at a rate proportional to their current value, which is represented by a more complex formula. This formula generally takes the form Y=Ce^(kt), where Y is the final amount, C is the initial amount, e is the base of the natural logarithm (approximately equal to 2.71828), k is the rate of growth or decay, and t is time.
In biology and population dynamics, exponential growth is illustrated by Curve A, which shows a population increasing rapidly over time - the hallmark of an exponential growth curve. In contrast, logistic growth, as shown by Curve B, depicts a population increasing until it reaches a limit known as the carrying capacity of its environment, where growth levels off. This gives logistic growth its characteristic S-shaped curve. Initially, logistic growth may resemble exponential growth, but due to limiting factors such as resources and predation, population growth eventually slows and stabilizes.
Exponential growth can occur in a population where there are adequate resources and minimal environmental resistance, allowing the population size to increase at an ever-accelerating rate. This scenario is less common in nature, where resources are typically limited, and other factors tend to eventually limit growth, resulting in the logistic growth model being more representative of most population dynamics.
In summary, the correct equation for exponential growth and decay contains additional parameters beyond just a constant, and the formula Y=C does not reflect the nature of exponential change. The final answer to the question is Option B: False.