Name: bacterial doubling in exponential growth
Uploaded: 2026-01-12T12:24:51.000Z
Duration: 1 min 29 s
Channel: JoVE

Cell populations in bacterial cultures are often modeled as exponential functions. Here, P of t shows the population function at time t, C shows the initial population, and k is the growth constant.The initial population at time zero is given; substituting this into the population function gives the value of C.Now this C is substituted back into the population function, leaving one unknown parameter.Dividing both sides by 50 and then applying the natural logarithm gives the value of k.The population at 1.5 hours is known. Substituting known values into the equation gives the value of k.This gives the population function with the known constants.The objective is to find the number of bacteria and the rate of growth at 3 hours.To find the rate of growth, the derivative of the population function is taken, which is equal to the growth constant multiplied by the population function itself.First, to find the number of bacteria at 3 hours, substitute three into the population function. This gives an estimated cell count.Then, substituting this value into the derivative of the population function gives the rate of growth.

exponential growth

Bacterial populations exhibit exponential growth when conditions such as nutrient availability and temperature are favorable. In this phase, cells reproduce through binary fission, where each cell divides into two identical daughter cells. This process causes the population to double at regular intervals, resulting in a growth rate that is directly proportional to the current number of cells. As the population increases, the number of new cells formed during each generation also grows, creating a steep rise in total cell count over time.Exponential growth is highly predictable under constant conditions, as the doubling time remains unchanged regardless of the starting population size. This property allows scientists to estimate how quickly bacterial cultures will expand in laboratory or industrial processes. For example, a small initial population can rapidly reach millions of cells within a few hours if nutrients remain abundant.Understanding exponential growth is essential in many fields, including medicine, where it helps explain how infections can escalate quickly if left untreated. It is also critical in biotechnology applications that rely on bacterial cultures for production. By recognizing the factors that sustain or limit exponential growth, researchers can better manage bacterial populations and design effective strategies for control or cultivation.

Exponential Growth

Bacterial populations exhibit exponential growth when conditions such as nutrient availability and temperature are favorable. In this phase, cells ...

Education

JoVE Core

Calculus

Unit

Differentiation Rules

KEY TERMS AND CONCEPTS

bacterial doubling in exponential growth

Bacterial populations can grow by doubling when conditions are favorable. When nutrients and temperature support growth, cells divide by binary fission. In binary fission, one cell splits into two identical daughter cells. This makes the population rise quickly.

During exponential growth, the growth rate depends on how many cells are already present. As the population gets larger, more new cells are formed in each generation. The result is a steep increase in total cell count over time. The doubling time stays the same as long as conditions remain constant.

This pattern is predictable, which helps scientists estimate how fast bacterial cultures will expand in lab or industrial settings. A small starting population can reach millions of cells within a few hours if nutrients stay abundant. Exponential growth also matters in medicine because infections can escalate quickly if they are not treated. It is important in biotechnology as well, where bacteria are used for production. By understanding what supports or limits this growth, researchers can better control or culture bacterial populations.

Bacterial Doubling in Exponential Growth

derivatives of simple functions

Slope Rules for Simple Functions

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the product rule

Derivative of a Changing Rectangle

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the quotient rule

Differentiating Ratios with the Quotient Rule

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derivatives of the trigonometric functions

derivatives-of-the-trigonometric-functions

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limits on trigonometric functions

Trigonometric Limits for Derivatives

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the chain rule

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the chain rule: problem solving

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implicit differentiation

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second derivatives of implicit functions

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implicit differentiation: problem solving

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derivatives of logarithmic functions

Natural Log Derivatives and Real-World Uses

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logarithmic differentiation

Differentiating Tire Stress with Logs

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the number e as a limit

e from Natural Log Derivatives

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derivatives of inverse trigonometric functions

derivatives-of-inverse-trigonometric-functions

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application of rates of change

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Bacterial populations can grow by doubling when conditions are favorable. When nutrients and temperature support growth, cells divide by binary fission. In binary fission, one cell splits into two identical daughter cells. This makes the population rise quickly. During exponential growth, the growth rate depends on how many cells are already present. As the population gets larger, more new cells are formed in each generation. The result is a steep increase in total cell count over time. The...

related rates

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linearization and approximation

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application of linearization and approximation

application-of-linearization-and-approximation

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hyperbolic functions

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inverse hyperbolic functions and their derivatives

inverse-hyperbolic-functions-and-their-derivatives

Deriving the Slope of a Catenary Curve

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hyperbolic and inverse hyperbolic functions: problem solving

hyperbolic-and-inverse-hyperbolic-functions-problem-solving

Tangent Lines on a Hyperbolic Arch

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key terms and concepts

Learn how bacteria double by binary fission during exponential growth, why the population rises so fast, and how this matters in labs, medicine, and biotechnology.

Bacterial Doubling in Exponential Growth | JoVE K12

The JoVE Core Calculus collection provides a comprehensive visual guide to the entire calculus sequence, seamlessly connecting mathematical theory to real-world applications in physics and economics. Through dynamic animated lessons, the course transitions smoothly from foundational single-variable concepts to advanced multivariable topics. Students will explore everything from standard differentiation and integration to spatial vectors, multi-dimensional derivatives, and complex vector fields. By breaking down abstract coordinate systems, infinite series, and spatial motion, this structured approach builds the robust analytical skills and advanced mastery essential for STEM success.

calculus

Bacterial Doubling in Exponential Growth

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