Algebraic expressions are really important for understanding how populations grow. They help us show and predict changes in population over time. By using these expressions, we can make equations that clearly explain the way population grows.

Key Concepts

1. Exponential Growth:
   Population growth is often shown using something called an exponential function. For example:
   $P(t) = P_0 e^{rt}$
   In this equation:

   • $P(t)$ is the population at a certain time ($t$)
   • $P_0$ is the starting population
   • $r$ is the growth rate
   • $e$ is a special number in math called Euler's number

2. Illustration:
   Let’s think about a town with a starting population of 1,000 people and a growth rate of 2%. We can use our equation to find out what the population will be after a few years:
   $P(5) = 1000 e^{0.02 \times 5}$

3. Applications:
   Using algebraic expressions helps us look at different situations. For example, we can see how a change in the growth rate can happen if the environment changes or if resources are limited. This is helpful not just for understanding what happened in the past but also for planning what might happen in the future.

In summary, algebraic expressions are strong tools that help us see how populations change. They prepare us to face real-world problems.