"Why do we use the form f(t)=ae^kt for exponential growth and decay? Why will we include the e^k? Would not or not it's simpler to definitely use f(t)=apt wherein p is the proportion growth according to time. Is there a reason why the convention is to apply f(t)=ae^kt?"

Francis Oliver

Francis Oliver

Answered question

2022-10-22

Why do we use the form f ( t ) = a e k t for exponential growth and decay?
Why will we include the e k ?
would not or not it's simpler to definitely use f ( t ) = a p t wherein p is the proportion growth according to time.
Is there a reason why the convention is to apply f ( t ) = a e k t ?

Answer & Explanation

Taxinov

Taxinov

Beginner2022-10-23Added 18 answers

The choice of base is arbitrary, but the primary reason is likely that the defining equation for the system looks like
d f d t = k f .
This means that the rate of growth of the population is proportional (proportionality k) to the population at a given time. The solution is f ( t ) = a e k t . It can be re-expressed as you said, but there is no benefit.

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