Time, t, is in the exponent, and that's why the change of S called "exponential growth".  How the "proportional to the current size" comes in is shown below.

The relative speed of the growth is an "irrelevant parameter," which means that it might be very fast and it might be very slow.  The meaning of exponential growth lies in a different dimension of meaning.
 

People reproducing at the same rate across the population will result in exponential growth of population.  The current constant of proportionality for human population growth is high enough that "astronomical" is a literally correct term for the growth rate we could expect in not too many centuries—certainly in a tiny fraction of the age of our species.  Physicist Harrison Brown has lent his name to the date that, if human population could continue its curent rate of population growth, human bodies would solidly pack the surface of the Earth and would be streaming away from the surface at the speed of light.

That's the "Harrison Brown date." (Let's leave it as an exercise to calculate when it is.)  Brown's point is, of course, that something will intervene before that date.  Well before that date!

When we ignore the pernicious possibilities for that "something," we surround ourselves with an aura of ignorance.  That's an aura that should probably strike terror in the hearts and souls of those making the important decisions...but it's an aura that's too seldom seen. 

Ignorance is bliss...isn't it?
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

species is a "fundamental category of taxamonic classification, ...an organism belonging to such a category,...a kind, variety or type."  (American Heritage Dictionary.)

In "Herpes simpletonisus," Herpes is the genus and simpletonisus is the species.

species  is both plural and singular.

specie  is coined money.
 
 
 
 
 
 
 

.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

epicenter is "the part of the earth's surface directly above the origin of an earthquake."  (American Heritage Dictionary)

Most news reporters associate "epicenter" with earhquakes, but don't know its meaning.  They are trained to use vivid, colorful language (exaggerate) and sense that calling the origin of anything an "epicenter" will make it sound big and important—and make themselves sound erudite.  To anyone in the know it simply surrounds the reporter with an aura of ignorance.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

parameter   a “fad word…constantly being misused by persons who apparently think it means ‘limits’ or ‘perimeter’ or ‘boundary-line’.” (Harry Shaw, in Dictionary of Problem Words and Expressions)  Its misuse surrounds the misuser with an aura of confusion. 

"...a varable or an arbitrary constant appearing in a mathematical expression..."  (American Heritage Dictionary)   One of the most common indicators of an aura of blissful ignorance is the ignoring of all but one out of many influences or parameters that are essential to understanding the fixes we get ourselves into. 
 
 

We have a problem here.  Usage has now established "a fixed limit or boundary" as another meaning for parameter.  So we have a lesson here, too.  Parameter entered the language from mathematics, where its use and meaning was familiar, important, and a concept that is obvious to users of mathematics.  But it is mathematics, Devlin's "fourth level of abstraction."  That level of abstraction is "ivory towered and quite out of touch with the real world" to those who have yet to take enough second glances to see what's there.  People heard the word often, but the meaning the mathematicians meant was missing--the route from perceptions to parameters not taken.  The much more concrete meaning of perimeter replaced the original meaning of parameter.  Many of the abstractions of science and mathematics suffer such substitutions when they are used in the wider world.  It's the words that get used, not the concepts. We also have a deeper lesson, one of great importance.  Many of man's most serious problems stem from failure to see the multi-element nature of those problems.  (A lot of pseudosciene does, too.)  Understanding multiple parameters is necessary (though probably not sufficient) for solving those problems.

aura  "An invisible breath or emanation...a distinctive air or quality that characterizes a person or thing.  (American Heritage Dictionary.)

Many who are not "seeing" the abstractions of science have recently (long after Maxwell,anyway) discovered that they can "see" the invisible emanations and distinctive airs that characterize people they look at.  They did discover that the high-voltage corona discharge that can ionize the air about sharply curved parts of a conductor (nicely explained by Maxwell's equations) can also expose photographic film.  They see those photgraphic patterns as corroborating their wondrous ideas of "Aura,"  A lot of folklore has developed about this Aura.

Devlin's "fourth level of abstraction" is also something some people can "see."  And when seen, it can reveal a lot about individual people.  See the "seer" and see the non-"seer" we describe as both try themselves to see the answer to Wason's card selection problem:  HERE

So...here's a little project the world really needs:

 

Let's develop an "Aura Detection Kit" which can help us all see what my colleague saw before he attacked the pseudoscience at the seminar.   He could predict how some people will likely confuse necessity and sufficiency, confuse all with some, and do other improper things with Boolean implication, on the basis of the Aura he could see emanated by the thinking they "obviously" were not doing.