Algebra is really important for understanding how populations grow and change over time. By using math formulas, we can see how many people there might be in the future. This is useful for things like economics, city planning, and environmental studies.

Key Ideas About Population Growth

1. Exponential Growth:

   • This means that the population can grow very fast because more and more people are being added.
   • We use a formula to show this growth: $P(t) = P_0 e^{rt}$ Here’s what the parts mean:
   • $P(t)$ = future population size
   • $P_0$ = starting population size
   • $r$ = growth rate (shown as a decimal)
   • $t$ = time in years

2. Example:

   • Let’s say there’s a population of 1,000 people that grows at a rate of 2% (which is 0.02). After 10 years, we can find out how many people there will be: $P(10) = 1000 \times e^{(0.02) \times 10} \approx 1,221.40$ So, after 10 years, the population would be about 1,221 people.

3. Sustainability:

   • Understanding how populations grow helps us plan for resources. For example, in 2020, the world's population was about 7.8 billion people. It’s predicted that by 2050, we might reach 9.7 billion people.

In short, algebra gives us important tools to understand and analyze how populations change. This is crucial for making smart decisions in the future.