Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Population Growth and Logistic Models**

**Scenario:**
Suppose a population grows according to a logistic model with an initial population of 200 and a carrying capacity of 2,000. If the population grows to 500 after one year, what will the population be after another three years?

**Explanation:**
In this scenario, we are using a logistic growth model to predict population changes over time. Logistic growth considers the carrying capacity, which is the maximum population size that the environment can sustain. 

- **Initial Population:** 200
- **Carrying Capacity:** 2,000
- **Population after 1 Year:** 500

The task is to determine the population size after an additional three years. Logistic growth is characterized by an initial period of rapid growth when the population is far below the carrying capacity, followed by a slowdown as the population approaches the carrying capacity.

To solve this problem, one would typically use the logistic growth equation and solve for the time variable, continuing the calculation based on given parameters.
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Transcribed Image Text:**Population Growth and Logistic Models** **Scenario:** Suppose a population grows according to a logistic model with an initial population of 200 and a carrying capacity of 2,000. If the population grows to 500 after one year, what will the population be after another three years? **Explanation:** In this scenario, we are using a logistic growth model to predict population changes over time. Logistic growth considers the carrying capacity, which is the maximum population size that the environment can sustain. - **Initial Population:** 200 - **Carrying Capacity:** 2,000 - **Population after 1 Year:** 500 The task is to determine the population size after an additional three years. Logistic growth is characterized by an initial period of rapid growth when the population is far below the carrying capacity, followed by a slowdown as the population approaches the carrying capacity. To solve this problem, one would typically use the logistic growth equation and solve for the time variable, continuing the calculation based on given parameters.
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