Calculus helps us understand how populations grow and change over time. Here are some simple ways it does this:

1. Differential Equations: We can use a math formula to describe how a population grows. It looks like this: $\frac{dP}{dt} = rP$. In this formula, $P$ means the size of the population, $t$ is time, and $r$ is how fast the population is growing.

2. Exponential Growth: Sometimes, populations can grow very quickly. We can write this growth with another formula: $P(t) = P_0 e^{rt}$. This shows that under the right conditions, populations can really explode!

3. Logistic Growth: In real life, there are limits to how much a population can grow. We can use the logistic model to account for these limits. The formula is: $P(t) = \frac{K}{1 + \frac{K - P_0}{P_0} e^{-rt}}$. Here, $K$ represents the maximum population the environment can support. This helps us make better predictions.

These models are useful for things like city planning, protecting nature, and managing resources!