What are biological or biochemical processes that are described (stochastically or deterministically) by exponential function f ( x ) = e a x ? What about examples that are not related to the population growth? I'm especially interested in biochemical examples.

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What are biological or biochemical processes that are described (stochastically or deterministically) by exponential function   f  (  x  )  =      e          a      x      ? What about examples that are not related to the population growth? I&#039;m especially interested in biochemical examples.

Aliya Moore · Accepted Answer

whenever a process evolves at a speed proportionnel to its own advancement, it satisfies the differential equation y′=ay which leads to exponential solutions.this is a very basic model for all kind of population growth (as you&#039;d say that the bigger the population is, the more baby they make per time unit).it is universal in the sense that if y satisfies a more complicated evolution equation y′=f(y) near an equilibrium point (for example, if you have a very small initial population, or a starting process) then linearizing this equation you obtain something like       y    ′    ≈      f    ′    (      y    0    )  y where       y    0   is the equilibrium point.Addendum : radioactive decay follows a decreasing exponential law because of the time-independance nature of the probability for a particle to split.Basic equations in kinetic chemistry are exponential laws (though they get more complicated for complex reactions), I suspect mainly because of the universal property I mentionned : it is &quot;the most simple evolution to an equilibrium state&quot; in a sense.

Ty Gaines · Accepted Answer

When a drug is eliminated from the body, typically that is described by giving a &quot;half life&quot; ... which means it is an exponential decay   C      e          a      t       with a&amp;lt;0. Then T is the half-life if       e          a      T        =  1      /    2, so it is related to the constant a.

What are biological or biochemical processes that are described (stochastically or deterministically) by exponential function f(x)=e^ax? What about examples that are not related to the population growth? I'm especially interested in biochemical examples.

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