Sequences are really interesting when it comes to predicting how populations grow. We’ve talked about this in class, so let me break it down for you:

1. Understanding Growth Rates: In biology, populations can grow at certain rates. This is often shown through sequences.

   For example, if a population grows by a steady percentage, like 5%, we use something called geometric sequences.

   Let's say we start with 100 rabbits. Here’s how the population would look over the years:

   • Year 1: 100 rabbits × 1.05 = 105 rabbits
   • Year 2: 105 rabbits × 1.05 = 110.25 rabbits
   • Year 3: 110.25 rabbits × 1.05 ≈ 115.76 rabbits

2. Finding Patterns: Sequences help us see patterns over time. After a few years, you might notice that the rabbit population doesn’t just grow slowly; it can start to grow faster and faster!

3. Making Predictions: We can use formulas with sequences to guess how many rabbits will be around in the future. For example, to find out how a population grows quickly, we can use this formula:

   [ P = P_0 \cdot r^t ]

   In this formula:

   • ( P_0 ) is the starting population,
   • ( r ) is the growth rate, and
   • ( t ) is the amount of time.

In short, sequences are powerful tools that help us predict how populations might grow or shrink. This is really important for things like managing wildlife or planning cities. It's amazing how math can help us understand real-life problems!