The second graph presented in the image below shows the survivorship of whales.
As we can see, the population grows rapidly after the calves reach adulthood, but the environmental factors limit the growth of the population and the population growth reached a plateau after a period of intense growth.
The process is called denaturation.
I hope this helped :)
I'm not exactly sure what specifically you are asking for in relationship to balancing equations, but I have some examples with working out so you can examine them and try to go through the steps with them.
Hope this helps! <3