Under perfect conditions, E. coli bacteria would cover the entire earth in a matter of days. Which of the following types of models is the best for explaining this type of growth?

The growth of a bacterial population, such as E. coli, under ideal conditions with unlimited resources is a classic example of exponential growth. In this model, the rate of population increase is proportional to the current population size. Each bacterium divides into two, causing the population to double at regular intervals (e.g., 1, 2, 4, 8, 16...). This leads to an extremely rapid, accelerating increase, which is accurately described by an exponential function (J-shaped curve). The scenario of covering the earth in days highlights this explosive growth characteristic.

A. Linear: A linear model represents constant, additive growth (e.g., adding 100 bacteria per hour), not the multiplicative, doubling growth seen in reproduction.
B. Logarithmic: A logarithmic model describes growth that starts quickly and then slows down as it approaches a limit, the opposite of the accelerating growth described.
C. Polynomial: While polynomial models can show rapid growth, the exponential model specifically describes a growth rate proportional to the current value, which precisely fits population doubling.

1. MIT OpenCourseWare. (2011). 7.01SC Fundamentals of Biology

Fall 2011. Session 26: Population Ecology. The course materials explain that under conditions of unlimited resources

a population exhibits exponential growth

modeled by the equation dN/dt = rN. Bacteria are used as a primary example. (Available at: MIT OCW

Fundamentals of Biology

Ecology I: Populations).

2. Zwietering

M. H.

Jongenburger

I.

Rombouts

F. M.

& van 't Riet

K. (1990). Modeling of the bacterial growth curve. Applied and Environmental Microbiology

56(6)

1875–1881. Section: "Introduction

" Paragraph 1. This paper discusses various mathematical models for bacterial growth

identifying the initial

unconstrained phase as exponential. (DOI: https://doi.org/10.1128/aem.56.6.1875-1881.1990).

3. University of California

Davis. (n.d.). BioSci 2B: Population Growth and Regulation. Chapter 45.2: Population Growth Models. The text explicitly states

"Bacteria are a prokaryote that reproduces by fission

and for many bacterial species

the doubling time is about an hour. This is an example of exponential growth."