Question
The graph below shows two different deer populations over the same ten year period.
Deer Population
mc026-1.jpg
Which of the following answers is the best description for the deer population with the greatest growth rate:
The blue line shows a deer population that grew with an exponential growth rate. In the first year the population increased by only one deer, but between years seven and eight the population grew by two deer, showing that the growth rate continuously doubles.
The blue line shows a deer population that grew with a linear growth rate, because the graph shows that the population increased by approximately one deer per year.
The red line shows a linear growth rate, because an approximate straight line estimates a growth rate of five deer per year.
The red line demonstrates an exponential growth rate, because the growth rate for the deer population is itself continuously increasing.
Deer Population
mc026-1.jpg
Which of the following answers is the best description for the deer population with the greatest growth rate:
The blue line shows a deer population that grew with an exponential growth rate. In the first year the population increased by only one deer, but between years seven and eight the population grew by two deer, showing that the growth rate continuously doubles.
The blue line shows a deer population that grew with a linear growth rate, because the graph shows that the population increased by approximately one deer per year.
The red line shows a linear growth rate, because an approximate straight line estimates a growth rate of five deer per year.
The red line demonstrates an exponential growth rate, because the growth rate for the deer population is itself continuously increasing.
Answers
GPT-4o mini
To determine the best description of the deer population with the greatest growth rate based on the information provided, let's analyze the options:
1. **Blue Line - Exponential Growth**: The assertion states that in the first year the population increased by one deer, and between years seven and eight it grew by two deer, suggesting the growth rate doubles. However, exponential growth typically means that the rate of growth increases more dramatically over time. The description does not adequately define a true exponential increase.
2. **Blue Line - Linear Growth**: This option claims that the blue line shows a linear growth rate, with the population growing by approximately one deer per year. If this is consistently true, it does indicate a linear growth rate, but does not depict the greatest growth rate among the two populations.
3. **Red Line - Linear Growth**: This asserts an approximate straight-line growth of five deer per year, which is plausible if the population increases consistently. However, linear growth will not exceed exponential growth in long-term scenarios.
4. **Red Line - Exponential Growth**: This statement claims that the red line shows an exponential growth rate with a continuously increasing growth rate. If the population grows faster over time, which is characteristic of exponential growth, then this could indicate the red line has the greatest growth rate.
Based on the typical characteristics of linear versus exponential growth:
- **Exponential growth** increases in a way that becomes more significant over time, while **linear growth** adds a constant amount each period.
- If we are considering which population has the greatest growth rate, the last description regarding the red line suggests that its growth rate increases continuously, thus it is likely the one with the greatest growth potential.
Therefore, the best description for the deer population with the greatest growth rate would be:
**The red line demonstrates an exponential growth rate, because the growth rate for the deer population is itself continuously increasing.**
1. **Blue Line - Exponential Growth**: The assertion states that in the first year the population increased by one deer, and between years seven and eight it grew by two deer, suggesting the growth rate doubles. However, exponential growth typically means that the rate of growth increases more dramatically over time. The description does not adequately define a true exponential increase.
2. **Blue Line - Linear Growth**: This option claims that the blue line shows a linear growth rate, with the population growing by approximately one deer per year. If this is consistently true, it does indicate a linear growth rate, but does not depict the greatest growth rate among the two populations.
3. **Red Line - Linear Growth**: This asserts an approximate straight-line growth of five deer per year, which is plausible if the population increases consistently. However, linear growth will not exceed exponential growth in long-term scenarios.
4. **Red Line - Exponential Growth**: This statement claims that the red line shows an exponential growth rate with a continuously increasing growth rate. If the population grows faster over time, which is characteristic of exponential growth, then this could indicate the red line has the greatest growth rate.
Based on the typical characteristics of linear versus exponential growth:
- **Exponential growth** increases in a way that becomes more significant over time, while **linear growth** adds a constant amount each period.
- If we are considering which population has the greatest growth rate, the last description regarding the red line suggests that its growth rate increases continuously, thus it is likely the one with the greatest growth potential.
Therefore, the best description for the deer population with the greatest growth rate would be:
**The red line demonstrates an exponential growth rate, because the growth rate for the deer population is itself continuously increasing.**