## The Biology Project > Biomath > Quadratic Functions > Applications > Logistic Model

Logistic Population Model Scanning electron micrograph of the bacteria Heliobacterium chlorum. Photo credit: F. R. Turner, Indiana University, Bloomington/ Courtesy: National Science Foundation. The logistic model of population growth assumes that the growth rate of the population decreases linearly with population size. In particular, the logistic equation gives the instantaneous rate of change of a population (ΔN) as, where r > 0 is the growth rate of the population in the absence of intraspecific competition and α > 0 is the per individual effect of competition. ΔN represents the rate at which the population is growing/decaying at any instant in time. For example, a population of microorganisms may grow at a rate of 10 microorganisms per day exactly two days after the population is innoculated.

Using the logistic equation, answer the following questions.

Write the logistic equation in standard form.

Find the value of N such that the instantaneous rate of population change is zero.

Use the logistic equation to find the carrying capacity of the environment (K).

Find the value of N where the instantaneous rate of population change is maximized.

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The Biology Project > Biomath > Quadratic Functions > Applications > Logistic Model

The Biology Project
Department of Biochemistry and Molecular Biophysics

The University of Arizona

May 2006
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