Exponential applications

growth/increase/appreciation or decay/decrease/depreciation
Discrete: n steps or time units Continuous
A(n) = A0(1±r)n A(t) = A0ekt
Amount A as a function of n steps or time intervals.
the 1 means 100%, the same.
± growth/decay rate r per step.
multiply itself n times.
then of the initial amount A0 		Amount A as a function of t time
A0 :initial amount
k = ln(1/2) / doubling_or_halving time.
Growth: k>0. Decay: k<0

A0 = 1 means 100%, then the function results are multiples or fractions of the initial amount.

Each film of tinted plastic blocks 10% of the light passing through it.
which means 90% of the light passes through.
The fraction f of light that passes through n successive films is:
f(n) = (1-.10)n = (0.90)n

How much of the light passes through 2 films?    How much is blocked?
Is the amount blocked by two films twice the amount blocked by one film?
How much of the light passes through 3 films?    How much is blocked?
Is the amount blocked by three films thrice the amount blocked by one film?
How much of the light passes through 5 films?    How much is blocked?
How much of the light passes through 10 films?    How much is blocked?
Is the amount blocked by 10 films twice the amount blocked by 5 films?

An initial amount of money A0 grows 10% each time unit (i.e. compound interest rate r is 10%).
After n time units, the money will accumulate to:
A(n) = A0(1+.10)n
This means one compounding period per time unit.

Atmospheric pressure p (in mm of Hg) as a function of height h (in km) above sea level.
p(h) = 760e-0.145h

What is the pressure at sea level?
What is the pressure 1 km above sea level?
What is the pressure one mile high?
What is the pressure at the summit of Fuji-san (3776m)?
What is the pressure at the summit of Mt Everest (8849m)?

k = ln(1/2) / halving_h
So: halving_h = ln(1/2) / k =

Our Atmosphere