What is the relationship between the carrying capacity and productivity of an an ecosystem

Explanation:

Carrying capacity refers to the maximum number of individuals of a certain species an environment can maintain in the long-term.

Factors that will determine carrying capacity include amount of water available in the environment, geographic size of environment, energy sources available, and so forth.

The image below shows the general idea of carrying capacity and population size:

The reality is often not so simple, as populations can overshoot their carrying capacity. When this happens, it takes some time for the population numbers to decrease. Thus, graphs more realistically resemble the one below:

Over time and with no disturbances, the population will generally max out at the carrying capacity. It is also important to remember that environments may not be unchanging, especially in certain time scales. For example, an increase in rainfall one year may mean that there is far more standing water available in the environment. Thus, mosquito populations will temporarily increase as the carrying capacity for them allows for higher numbers.

the wires in the toaster turning red and the toast crisping and turning brown