Using Fibonacci sequences to understand how populations grow is really interesting! It connects the math we learn in school to real-life situations.

The Fibonacci sequence starts with the numbers 0 and 1. Then, each new number in the sequence is the sum of the two numbers before it. So, it looks like this: 0, 1, 1, 2, 3, 5, 8, 13, and keeps going.

In nature, some animals, like rabbits, show growth patterns that follow the Fibonacci sequence. Here’s a simple way to see how this works:

1. Starting Pair: Imagine you have one pair of rabbits. Each month, they create a new pair.

2. Growing Population: In the first month, you have 1 pair of rabbits. The next month, that pair has another pair, so now you have 2 pairs. The month after, the first pair has another pair, and the new pair will start having babies by the next month.

3. Fibonacci Relation: You can model the number of rabbit pairs using the rule: $F(n) = F(n-1) + F(n-2)$ where $F(0) = 0$ and $F(1) = 1$. So, $F(n)$ tells you how many pairs there are at month $n$.

4. Estimating Numbers: If you want to guess how many rabbits there will be in the future, you can use this model. After 6 months, the population would be $F(6) = 8$ pairs.

5. Things to Keep In Mind: While this is a cool model, it’s important to remember that it assumes there are unlimited resources, like food and space. In real life, populations can get limited by these factors.

Overall, using Fibonacci sequences to study population growth shows us how math can help explain what's happening in the world around us. It's fascinating to see how numbers connect to nature!