An ecologist studies three populations within an ecosystem. Each population has an identical intrinsic growth rate (r max = 0.5). The population sizes and carrying capacities are shown in the graph. 1000 900 800 700 600 500 400 300 200 100 ㅇ A Population 1 Size - Carrying capacity What is the growth rate of Population C? Number
An ecologist studies three populations within an ecosystem. Each population has an identical intrinsic growth rate (r max = 0.5). The population sizes and carrying capacities are shown in the graph. 1000 900 800 700 600 500 400 300 200 100 ㅇ A Population 1 Size - Carrying capacity What is the growth rate of Population C? Number
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Author:Elaine N. Marieb, Katja N. Hoehn
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![# Ecological Population Growth Study
An ecologist studies three populations within an ecosystem. Each population has an identical intrinsic growth rate ( \( r_{max} = 0.5 \) ). The population sizes and carrying capacities are shown in the graph below.
## Graph Analysis
### Description:
- **X-axis:** Represents the three populations, labeled A, B, and C.
- **Y-axis:** Represents the number of individuals in each population, ranging from 0 to 1000.
- **Legend:**
- **Blue Bars:** Indicate the current population size.
- **Red Bars:** Indicate the carrying capacity, which is the maximum population size that the environment can sustain.
### Data:
- **Population A:**
- **Size:** Approximately 100 individuals.
- **Carrying Capacity:** Approximately 200 individuals.
- **Population B:**
- **Size:** Approximately 400 individuals.
- **Carrying Capacity:** Approximately 500 individuals.
- **Population C:**
- **Size:** Approximately 900 individuals.
- **Carrying Capacity:** Approximately 1000 individuals.
## Question:
What is the growth rate of Population C? _____
### Graph Interpretation:
The graph shows the difference between the current population sizes and their respective carrying capacities. The intrinsic growth rate (\( r_{max} \)), set to 0.5, is a constant factor for all populations. To calculate the growth rate of Population C, we'll utilize the provided intrinsic growth rate along with the current population size and carrying capacity.
### Calculation:
To find the growth rate of Population C, the following formula can be used:
\[ \text{Growth Rate} = r_{max} \times \left(1 - \frac{\text{Population Size}}{\text{Carrying Capacity}}\right) \times \text{Population Size} \]
Substitute the values for Population C:
\[ \text{Growth Rate} = 0.5 \times \left(1 - \frac{900}{1000}\right) \times 900 \]
\[ \text{Growth Rate} = 0.5 \times (1 - 0.9) \times 900 \]
\[ \text{Growth Rate} = 0.5 \times 0.1 \times 900 \]
\[ \text{Growth Rate} = 0.5 \times 90 = 45 \]
Thus,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3864dd7c-4d81-415c-860d-ecabf4ae9b4b%2F8a0d7b1c-a96e-46ca-aaa7-5aea047aa076%2F9kfmbsg.jpeg&w=3840&q=75)
Transcribed Image Text:# Ecological Population Growth Study
An ecologist studies three populations within an ecosystem. Each population has an identical intrinsic growth rate ( \( r_{max} = 0.5 \) ). The population sizes and carrying capacities are shown in the graph below.
## Graph Analysis
### Description:
- **X-axis:** Represents the three populations, labeled A, B, and C.
- **Y-axis:** Represents the number of individuals in each population, ranging from 0 to 1000.
- **Legend:**
- **Blue Bars:** Indicate the current population size.
- **Red Bars:** Indicate the carrying capacity, which is the maximum population size that the environment can sustain.
### Data:
- **Population A:**
- **Size:** Approximately 100 individuals.
- **Carrying Capacity:** Approximately 200 individuals.
- **Population B:**
- **Size:** Approximately 400 individuals.
- **Carrying Capacity:** Approximately 500 individuals.
- **Population C:**
- **Size:** Approximately 900 individuals.
- **Carrying Capacity:** Approximately 1000 individuals.
## Question:
What is the growth rate of Population C? _____
### Graph Interpretation:
The graph shows the difference between the current population sizes and their respective carrying capacities. The intrinsic growth rate (\( r_{max} \)), set to 0.5, is a constant factor for all populations. To calculate the growth rate of Population C, we'll utilize the provided intrinsic growth rate along with the current population size and carrying capacity.
### Calculation:
To find the growth rate of Population C, the following formula can be used:
\[ \text{Growth Rate} = r_{max} \times \left(1 - \frac{\text{Population Size}}{\text{Carrying Capacity}}\right) \times \text{Population Size} \]
Substitute the values for Population C:
\[ \text{Growth Rate} = 0.5 \times \left(1 - \frac{900}{1000}\right) \times 900 \]
\[ \text{Growth Rate} = 0.5 \times (1 - 0.9) \times 900 \]
\[ \text{Growth Rate} = 0.5 \times 0.1 \times 900 \]
\[ \text{Growth Rate} = 0.5 \times 90 = 45 \]
Thus,
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