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I wrote earlier:
By the way, you can also use  it to answer the question "where does space
begin?" Just set the equation for  density of the air:
density = exp(-altitude/34,000feet)
equal to 0  and solve for the altitude. :-)"

Bill you replied:
"Having little  success with modifying the formula with my math skills.
Trying to manipulate  the exponent and or find the nth root of zero has me
off in deep  space.
Did try the plug and chug method with the TI-30, and ran out of  computing
power approx. 1277 nm. Looks like with enough computing power it  could go on
like pi.  Interesting as I would have thought the value  would have been in
the 60-120 nm range."

Yep. It never ends. The  equation 0=exp(-altitude/34000feet) has no solution.
The atmosphere never ends.  It just gets thinner and thinner until it becomes
indistinguishable from the  interplanetary medium.

If you ever end up explaining this to a group of  students, one of them will
surely ask, "but, but isn't the International Space  Station in space??" Isn't
it? Well for various practical purposes, it is, yes.  It is so nearly in
freefall that for nearly all practical purposes the  astronauts are weightless and
free of the influence of air. But the station  actually experiences
considerable air resistance from the higher reaches of the  Earth's atmosphere even
"way up there". That air resistance slowly bleeds away  its orbital energy. The
station would burn up in thicker air within a year and a  half or so unless
actively reboosted every couple of months. That, of course, is  exactly what
happened to the abandoned US space station Skylab back in 1979 when  it rained
debris over Australia and the abandoned Soviet space station Salyut 7  back in
1991 which rained its debris over Argentina.

Sorry for getting  off-topic. Just to help understand the barometric pressure
issue, there is  another way of writing the equation. We can change the
"base" from e to 2 and  write it as
relative density=(1/2)^(altitude/24000feet).
It might  not look much better and really it is exactly the same content as
the original  equation, but the verbal description is much easier to understand
for most  people. This equation is saying that the density is cut in half
every 24,000  feet. It's a simple "geometric progression". And when you start out
with any  non-zero number (air density at sea level in this case), no matter
how many  times you cut it in half, you will never get to zero.

-FER
42.0N  87.7W, or 41.4N 72.1W.
www.HistoricalAtlas.com/lunars

   

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