Linear equations can be a simple way to predict how a population will grow. However, they have some big problems that can make their predictions really off.

1. What We Assume:

   • When we look at population growth, we often treat it as if it grows at a steady rate. This is shown with the formula $P(t) = P_0 + rt$.
   • In this formula, $P_0$ is the starting population, $r$ is the growth rate, and $t$ is the time.
   • This idea assumes there are unlimited resources and doesn’t take into account things like environmental changes, diseases, or economic issues.

2. The Real World Is Messy:

   • Many factors that affect population growth are not straightforward. Because of this, it can be hard to predict actual growth accurately.
   • Events like pandemics or changes in government policies can completely change the effectiveness of these simple equations over time.

3. Better Ways to Predict:

   • Using more complicated models, like logistic growth equations, can help us get better predictions.
   • Staying flexible and updating our models with current information can improve predictions and solve some of the problems with linear equations.