A national park has a current population of 2000 bison. They reproduce annually at a rate of 5%. Experts say the park can sustain a population of 10,000 bison. What is the current population 5 years from now?

To calculate the projected population of bison 5 years from now, given the initial population, growth rate, and carrying capacity, we can use the **logistic growth model**. This model accounts for limited resources in the environment (the park can sustain a maximum of 10,000 bison).

The formula for logistic population growth is:

\[
P(t) = \frac{K}{1 + \left(\frac{K - P_0}{P_0}\right) e^{-rt}}
\]

Where:
- \( P(t) \) is the population at time \( t \),
- \( K \) is the carrying capacity (10,000 bison),
- \( P_0 \) is the initial population (2,000 bison),
- \( r \) is the growth rate (5% or 0.05),
- \( t \) is the time in years (5 years).

Let's calculate the population \( P(5) \).

The projected population of bison in the national park 5 years from now is approximately **2,430** bison.

Would you like further details or have any questions about the calculation?

Here are some related questions to expand on this topic:
1. How would the population change after 10 years?
2. What happens if the growth rate increases to 7%?
3. How does the carrying capacity affect population growth?
4. Can this model be applied to other species with different growth rates?
5. How does the population change when the current population is much closer to the carrying capacity?

**Tip**: Logistic growth models are more accurate for populations with limited resources, as they take into account the environmental constraints.

Calculate the projected population of bison in a national park over 5 years, accounting for a 5% annual growth rate and a carrying capacity of 10,000 bison. Learn how to apply the logistic growth model to determine future population numbers. Suitable for students in Grades 10-12.

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