Question
Scientists have stocked Paulo's pond with a species of fish. The scientists note that the population has steadily decreased over a period of time until the population is approximately half of the original number of fish. If the number of fish is plotted on the y-axis and the amount of time on the x-axis, which of the following could result?
Answers
GPT-4o mini
To illustrate the situation you've described, we can consider the shape of the graph when plotting the fish population on the y-axis and time on the x-axis. Given that the population decreases steadily to about half of its original amount, we would expect the graph to display a downward trend over time.
Here are a few possible scenarios that could result in this outcome:
1. **Exponential Decay**: If the fish population decreases at a rate proportional to its current size, the graph would exhibit an exponential decay curve. This means that the population would drop quickly at first and then level off as it approaches zero.
2. **Linear Decrease**: If the fish population decreases by a consistent amount over equal intervals of time, the graph would show a straight line sloping downward. This would suggest a constant rate of decline.
3. **Logarithmic Decay**: Similar to exponential decay, but the initial decrease may be rapid and then slow down as time goes on. The graph would start steep and then flatten.
Given the context of "steady decrease" as mentioned in your statement, the most fitting representation would likely be either an exponential decay or a linear decrease, depending on the nature of that decrease:
- **Exponential Decay** might be more applicable if the decrease accelerates initially but slows down as the population approaches half.
- **Linear Decrease** implies a constant decline over time.
For a visual representation, you would see a curve that starts at a higher point on the y-axis (indicating the original fish population) and moves downward to about half that value on the y-axis, but remains steady after that, depending on how the population dynamics are modeled.
If you were given specific options for graphs, the one that depicts a steady decrease that reaches around half the original population would be the correct choice.
Here are a few possible scenarios that could result in this outcome:
1. **Exponential Decay**: If the fish population decreases at a rate proportional to its current size, the graph would exhibit an exponential decay curve. This means that the population would drop quickly at first and then level off as it approaches zero.
2. **Linear Decrease**: If the fish population decreases by a consistent amount over equal intervals of time, the graph would show a straight line sloping downward. This would suggest a constant rate of decline.
3. **Logarithmic Decay**: Similar to exponential decay, but the initial decrease may be rapid and then slow down as time goes on. The graph would start steep and then flatten.
Given the context of "steady decrease" as mentioned in your statement, the most fitting representation would likely be either an exponential decay or a linear decrease, depending on the nature of that decrease:
- **Exponential Decay** might be more applicable if the decrease accelerates initially but slows down as the population approaches half.
- **Linear Decrease** implies a constant decline over time.
For a visual representation, you would see a curve that starts at a higher point on the y-axis (indicating the original fish population) and moves downward to about half that value on the y-axis, but remains steady after that, depending on how the population dynamics are modeled.
If you were given specific options for graphs, the one that depicts a steady decrease that reaches around half the original population would be the correct choice.