In the Malthusian model, population grows exponentially while food production grows linearly. For the Rarotonga tribe, food production is enough to support 1,167 people at the subsistence level, and each year they are able to expand food production to accommodate another 46 people. Their population is only at 858 people, but it grows by 10% each year. Assuming each member of the tribe is living at the subsistence level, what will the population of Rarotonga be after 63 years?

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Chapter1: Financial Statements And Business Decisions
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### Malthusian Model and Population Growth

#### Concept Overview:
In the Malthusian model, population grows exponentially while food production increases linearly. This creates a scenario where, over time, the population may exceed the available resources, leading to potential challenges in sustaining the population.

#### Case Study: Rarotonga Tribe
- **Initial Conditions:**
  - The tribe's current population: 858 people
  - Existing food production supports: 1,167 people at the subsistence level

- **Growth Dynamics:**
  - **Food Production:** Increases linearly, expanding each year to support an additional 46 people.
  - **Population Growth:** Increases exponentially at a rate of 10% per year.

#### Problem Statement:
Given that each member of the tribe lives at the subsistence level, calculate the population of Rarotonga after 63 years.

#### Required Calculation:
To solve this problem, consider the exponential growth formula for population and the linear growth formula for food production. By comparing these, the population size and the adequacy of the food supply at different points in time can be determined.

**Note:** There are no graphs or diagrams included that need explaining in this scenario.

Would you like a detailed step-by-step solution on how to perform these calculations?
Transcribed Image Text:### Malthusian Model and Population Growth #### Concept Overview: In the Malthusian model, population grows exponentially while food production increases linearly. This creates a scenario where, over time, the population may exceed the available resources, leading to potential challenges in sustaining the population. #### Case Study: Rarotonga Tribe - **Initial Conditions:** - The tribe's current population: 858 people - Existing food production supports: 1,167 people at the subsistence level - **Growth Dynamics:** - **Food Production:** Increases linearly, expanding each year to support an additional 46 people. - **Population Growth:** Increases exponentially at a rate of 10% per year. #### Problem Statement: Given that each member of the tribe lives at the subsistence level, calculate the population of Rarotonga after 63 years. #### Required Calculation: To solve this problem, consider the exponential growth formula for population and the linear growth formula for food production. By comparing these, the population size and the adequacy of the food supply at different points in time can be determined. **Note:** There are no graphs or diagrams included that need explaining in this scenario. Would you like a detailed step-by-step solution on how to perform these calculations?
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