the population of certain species of fish is modeled by a logistic growth model with relative growth rate of k =0.3. One hundred fish  are initial introduced into the pond with maximum carrying capacity  of 500. assuming that fish are not harvested.

estimate the number of fish in the pond after 1 year

estimate the time it will take for there to be a 200 fish in the pond

calculate with handwritten

### Part 1: Estimate the number of fish in the pond after 1 year
Using the logistic growth model, after 1 year, the estimated number of fish in the pond is approximately **126 fish**.

### Part 2: Estimate the time it will take for the population to reach 200 fish
The estimated time for the population to grow to **200 fish** is approximately **3.27 years**.

(Note: The other solutions with complex values are not physically meaningful in this biological context.)

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### Follow-up questions:
1. How does the logistic model differ from exponential growth in fish population?
2. Can the logistic model predict what happens after reaching the carrying capacity?
3. What factors might affect the growth rate \( k \) in real-life scenarios?
4. How would the population change if the initial population were higher, say 200 instead of 100?
5. How is the time for the population to reach 300 fish different from 200 fish?

**Tip:** Logistic growth models are commonly used in ecology to represent population growth with limiting resources, such as food or space.

The population of certain species of fish is modeled by a logistic growth model with a relative growth rate of k = 0.3. One hundred fish are initially introduced into the pond with a maximum carrying capacity of 500, assuming that fish are not harvested. Estimate the number of fish in the pond after 1 year. Estimate the time it will take for there to be 200 fish in the pond.

Learn how to apply the logistic growth model to estimate the fish population in a pond. The initial population is 100 fish, with a growth rate of k = 0.3 and a carrying capacity of 500. After 1 year, the population is estimated to be 126 fish, and it will take approximately 3.27 years to reach 200 fish.

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