"Why is e so special? The number e (and the exponentiation function ex) appears in so many places in mathematics and engineering. There seem to be a multitude of applications of it. I want to know why. "

frobirrimupyx 2022-09-14 Answered
Why is e so special?
The number e (and the exponentiation function e x ) appears in so many places in mathematics and engineering. There seem to be a multitude of applications of it. I want to know why.
You can still ask an expert for help

Want to know more about Exponential growth and decay?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Yaritza Cardenas
Answered 2022-09-15 Author has 20 answers
Because very many of humanity's age-old mathematical interests ultimately converged towards it:
Arithmetic:
Addition begets multiplication; multiplication begets exponentiation; exponentiation begets e, seeing that by using reading it we inevitably arrive at the conclusion that this number is its most herbal base.
LCM ( 1 , 2 , 3 , , n ) n   tends to e as n tends towards infinity.
Geometry:
Circles and hyperbolas have been studied since ancient times; e is to the latter what π is to the former.Finance:
Examining the way in which banking interests are computed leads us to discovering the same quantity.Calculus:
The harmonic series has been studied since ancient times; its continuous equivalent is = log e x
The solution to f ( x ) = f ( x ) is a   e x , meaning that the exponential function is immune to the operations of differentiation and integration.

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-03-23
  • At the beginning of the year, there are 7650 individuals in a population of beavers whose per capita rate of for the year is 0.18. What is its population growth rate at the end of the year? 
asked 2022-09-18
A Bacteria Culture Contains 100 Cells and Grows at a Rate Proportional to its Size
A bacteria culture contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420.
a) Find and expression for the number of bacteria after t hours
P ( t ) = P ( 0 ) e k t = 100
b) Find the number of bacteria after 3 hours.
P ( t ) = P ( 3 ) e k 3 = (confused as to how to set this up)
d) When will the population reach 10,000?
asked 2022-02-01
Give an example of an exponential function in the form y=a×bx that is neither an exponential growth function nor an exponential decay function. Explain your reasoning.
asked 2022-09-12
A Bacteria Culture Grows with Constant Relative Growth Rate.
A micro organism culture Grows with consistent Relative boom rate. The micro organism count number become 400 after 2 hours and 25,six hundred after 6 hours.
a) What is the relative growth rate? Express your answer as a percentage.
Using this formula P ( t ) = P 0 e k t
t = t i m e
k = g r o w t h   r a t e
p 0 = i n i t i a l   a m o u n t
How do I calculate a formula with the information I have?
b) What was the initial size of the culture?
c) Find an expression for the number of bacteria after t hours
d) Find the number of cells after 4.5 hours
e) Find the rate of growth after 4.5 hours
f) When the population reach 50,000?
that is a self look at query. i've Calculus II subsequent semester and sincerely would like to have a clear method as to a way to solve a hassle inclusive of this.
asked 2022-01-19
Consider the model for exponential growth or decay given by A=A0ekt.
If k_____ , the function models the amount, or size,of a growing entity. If k_____ , the function models the amount, or size, of a decaying entity.
asked 2021-05-26

Tell whether the function represents exponential growth or exponential decay. Explain your reasoning. f(x)=4ex

asked 2021-06-26

State whether the equation represents exponential growth, exponential decay, or neither. y=0.823x

New questions