Exponential functions

Pure exponential growth

Pure exponential growth begins slowly, then literally explodes over time.

Quantity rises slowly, then much more rapidly as time passes

Pure exponential growth

Bacteria population tends to grow exponentially in a suitable environment.

Clumps of oval-shaped bacterial

Bacteria (photo credit: CDC US government)

Different growth rates result in different levels of growth at a particular point of time, but growth is still ultimately explosive (see below).

Plots showing lower growth rates result in slower, but still explosive growth

Various rates of exponential growth

Efficiency-Discounted Exponential Growth

Efficiency-Discounted Exponential Growth (EDEG) involved the consumption of a non-replenished resource over time by a system of reproducing agents.

Logistic Growth

In logistic growth, population tends to move towards a particular population level that reflects the carrying capacity of the system or environment.

Logistic growth (rises then levels off)

Logistic growth