How do I work with the exponential model #y = ae^(kt)#?

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Oct 5, 2015

Answer:

You work with the exponential model by learning its properties, and find an area for application.

Explanation:

The exponential models is one of the richest one in applications, it is unbelievable how it can be found in different areas, from biology to probability theory.

So:

#y(t) = a*e^(kt)#

The first parameter is "a", this parameter tells us where it touches the y-axis when time is zero, just remember that any number powered 0 is 1, then:

#y(t) = a*e^(0)=a#

The second parameter is "k", it tells you how fast it grows with time, the higher the value, the faster the function grows.
#y(t) = a*e^(kt)#. a is kept constant and k is increased, green is 0.1, and cyan 0.4. It was used Matlab, hold on to plot the multitple curves

If you are familiar with calculus, take the limit to -infinity, then it touches x-axis at -infinity, in practical terms, never!

In general people need to make a regression (i.e. find the exponential from a set of experiments), then it is useful:

#lny(t) = a + kt#

Just apply the logarithmic properties. Then you have a line.

Examples

Probability: exponential distribution

Exponetial

See for more: https://en.wikipedia.org/wiki/Exponential_distribution.

In ecology:

#N(t)=e^((a-b)*t)#

Where a is birth and b death rate.

Examples are plenty. This function is quite rich. you learn everyday from this simple function.

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Sep 20, 2015

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By having your own fashion-brand and hiring that model, for example.

Explanation:

But seriously, how to work with the exponential model?
By learning and using it.

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