Living Physics Portal: Biological applications of the exponential

Abstract: A set of homework problems for students to help them develop and understanding of the value and implication of the exponential function is a variety of active learning situations of biological relevance.

Resource Types: Homework, Restricted access

This resource by:

Edward Redish (he/him)

University of Maryland, College Park

What's different about this adaptation? Have added readings and problems that are specific to biochemical and cellular examples. More details

Adapted from original resource(s):

Exponential functions

Clicker question, Exam problem, Homework, In-class activity, Instructor supplement, Lab, Lecture materials, Restricted access

Vetted

Connect exponential equation to cooling, chemical reactions, metabolic rates and filtration rates

Human and Animal Physiology > Thermoregulation; Human and Animal Physiology > Renal/Urinary; Human and Animal Physiology > Metabolism

Thermo & Stat Mech > First Law > Heat Transfer; Electricity & Magnetism > DC Circuits > RC Circuits

Dawn Meredith

Christopher Shubert

TOPICS

Physics Topics:

Thermo & Stat Mech > Kinetic and Diffusive Processes > Diffusion

Thermo & Stat Mech > Probability

Life Sciences Topics:

Biochemistry > Proteins

Cross-cutting Biological Concepts > The Cell

Molecular and Cellular Biology > Cellular Dynamics

Math Topics:

Algebra; Exponentials and Logarithms; Graphical Analysis

FILES Download0

Biological applications of the exponential

Boltzmann factor problems with exponentials

Boltzmann -- physicist or chemist.pdf

Opening a channel - perhaps.pdf

Molecular polymorphism.pdf

Evaporating a membrane.pdf

Probability of molecular excited states.pdf

Workout - The Boltzmann distribution.pdf

Opening a channel - perhaps.url

Evaporating a membrane.url

Boltzmann - physicist or chemist.url

Molecular polymorphism.url

Probability of molecular excited states.url

Workout - The Boltzmann distribution.url

Debye length problems with exponentials and logarithms

Debye length change.pdf

Electric fields in solution.pdf

Electric fields in solution.url

Debye length change.url

Diffusion problems with exponentials

Nernst potential toy model.pdf

Random or not, here I come (MC).pdf

Random or not, here I come.pdf

Nernst potential toy model.url

Random or not, here I come.url

Random or not, here I come (MC).url

Boltzmann -- physicist or chemist.pdf

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INSTRUCTOR GUIDE

IMPLEMENTATION

Equipment required: Computers / software

Specific equipment needed: Problems are available on the web. Some problems require the use of an online graphing calculator.

Basic implementation tips & tricks: The homework, quiz, and clicker problems are drawn from multiple topics throughout the class. Seeing the same technique in different contexts can help students see the power of the math of exponentials and logarithms.

How does this resource fit into the flow of your course? An introduction to exponentials (readings, PPT slides) is given the first time an exponential topic arises. Later, problems with exponentials and logarithms are dropped into the flow of the class as appropriate.

PEDAGOGY

Pedagogical approach: Peer Instruction / Think-Pair-Share; Collaborative problem-solving; Mathematically-focused activities

Skills / Competencies: Functional dependence; Multiple representations; Interdisciplinarity

What insights or realizations do you hope students gain from this resource? That exponentials and logarithms are a powerful tools for helping to make sense of many situations of relevance to biology.

Why is this resource useful to life sciences students? In addition to exponentials and logarithms being common mathematical tools that are widely used in science, exponential examples are particularly valuable in helping students learn the general skills that help them blend a conceptual understanding of the physics with a multiple mathematical representations: symbolic math and graphs.

DISCUSSION

RELATED RESOURCES

THIS RESOURCE ADAPTED FROM

What's different about this adaptation? Have added readings and problems that are specific to biochemical and cellular examples.

More about how and why this resource was changed: I noted that some of the readings problems my team had developed for biological applications of the exponential fit as natural and potentially useful extensions to the existing work.