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EXPONENTIAL FUNCTIONS

General Model for Exponential Functions:

y = c (a)k(x-p) + b

c:  Initial value
a:  Growth factor for a > 1
a:  Decay factor for 0 < a < 1
k:  constant
b:  Constant
p:  Constant
x:  Number of period
y:  Amount at the end of the period

 


APPLICATIONS OF EXPONENTIAL FUNCTIONS

General exponential function:

y = c (a)x

x:  Number of growth or decay period
a:  Growth factor for a > 1
a:  Decay factor for 0 < a < 1
c:  Initial amount
y:  Future amount
Exponential growth
(doubling period):

A = A0 (2)t/d

A0 :  initial amount (t = 0)
A:  Amount at the end of time
t:  Time (s, min, hour, day, years, etc.)
(2):  Growth factor
d:  Doubling period (s, min, hour, day, years, etc.)
Exponential decay (half life):

A = A0 (1/2)t/h

A0 :  initial amount (t = 0)
A:  Amount at the end of time
t:  Time (s, min, hour, day, years, etc.)
(1/2):  Decay factor
h:  Half life (s, min, hour, day, years, etc.)
Population estimate:

P = P0bt

P0:  Initial population for t = 0
P:  Population after t years
b:  base (population growth if b >1;  population decrease if 0 < b < 1)
t:  time (years)
Exponential function with base e:

A = A0 ert

A0 :  initial amount (t = 0)
A:  Amount at time t
e:  base (e = 2.71828182...)
r:  constant (growth for r  > 0;  decay for r < 0)
t:  time
Compound Interest:

A = P (1+i)n

 
A:  Future amount
P:  Present amount
i:  Interest rate per compounding period
n:  Number of compounding period
Geometric sequence:

tn = a(r)n-1

 
tn:  nth term in the sequence
a:  First term
r:  Common ratio
n:  Number of terms