Assumed knowledge

This module builds upon the module Exponential and logarithmic functions. It assumes knowledge of that module and also the modules required for it:

Motivation

And so from hour to hour we ripe and ripe,
And then from hour to hour we rot and rot,
And thereby hangs a tale.

— William Shakespeare, As You Like It.

Almost everything in our world grows and decays. From the growth of organisms to their eventual death, from the growth of suns to their eventual supernovas, from the growth of crystals to the decay of radioactive isotopes, from the growth of animal populations to the decay of radio signals, from the growth of economic output to the depletion of resources, little in our world is stationary. As the ancient Greek philosopher Heraclitus said, 'all is in flux'.

Sometimes, we can describe processes of growth and decay — whether physical, chemical, biological or sociological — by mathematical models. These models are only approximations to the real world, but they can help us to understand it and make predictions about it.

One of the most common ways in which a quantity can grow or decay is exponentially. We primarily focus on exponential growth and decay in this module, but we also briefly consider other models and equations.

In the module Exponential and logarithmic functions, we developed exponential and logarithmic functions from a pure-mathematical point of view. We defined these functions rigorously and studied their properties, including derivatives, integrals and graphs. In this module, we take a more applied-mathematical point of view. We consider mathematical models of exponential growth and decay in other fields of science.

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