Pure · Exponentials & logarithms
Chapter 1 · 3
The idea
Exponential growth and decay models
Real-world models of the form N = N0 e^{kt} (or A = a + b e^{kt}): finding the starting value, fitting the rate constant to data with logs, interpreting parameters, rates and limiting values.
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Pure · Exponentials & logarithms
Exponential growth and decay models
Real-world models of the form N = N0 e^{kt} (or A = a + b e^{kt}): finding the starting value, fitting the rate constant to data with logs, interpreting parameters, rates and limiting values.
Why it works
Rate proportional to size
A cup of coffee sits at C in a C room. It cools fast at first, then slower and slower as it approaches room temperature — how do you write that as maths? The same shape turns up everywhere: populations grow faster the bigger they are, radioactive mass decays faster the more there is. Anything whose rate of change is proportional to its current size (or to its distance from a limit) follows an exponential model, in its plainest formKeep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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