x       y       Exp y   Ln y
1       2.71828 0
Curve Fitting--some general guidelines for interpretation.
2       1.1     3.00417 0.09531
1.2     3.32012 0.18232
Problem:  I have some data--how might I decide what sort of curve to try
to fit to it.
4       1.7     5.47395 0.53063
2.5     12.1825 0.91629
The nature of the data can suggest the type of curve.
6       2.9     18.1741 1.06471
4       54.5982 1.38629
If your concern is to forecast from your data:
8       6.1     445.858 1.80829
10.3    29732.6 2.33214
     unbounded with no upper bound:                                                                                             
try a linear, exponential, or logarithmic curve.                                                                                                
linear--increases in the future occur at the same rate as increases in the
present and past--                                                                                              
     the slope of the line is constant.                                                                                         

exponential--increases in the future occur at an increasing rate as time
     the slope of the line increases as time progresses.

logarithmic--increases in the future occur at a decreasing rate as time
     the slope of the line is decreasing.

A few types of interpretations:

Linear--index numbers in time series analysis--
     index numbers are used to relate a variable in one period of time to
the same variable in another
     period of time (the base period).  An index number is a relative
number describing data that 
     change over time (the data are a time series).
      Index numbers are often valuable in dealing with complicated data or
data of great magnitude.
     In practice, they are often used to capture economic
indicators--trends over time.
          Trend for the Index of Industrial Production
          Trend for the Wholesale Price Index --  source--Economic Report
of the President                        
          Trend in equipment expenditures of the Curve Fitting Computer
Company in millions of $$.                      
          Trend in overseas shipments of Eyepoint Needle Company in
millions of needles.                    
          Trend in the Consumer Price Index, 1980-1990; 1985=100.                       
               For example:                     
                            Year          Index                 
        1980            90
        1981            93
        1982            97
        1983            102
        1984            104
        1985            100
        1986            101
        1987            99
        1988            103
        1989            107
        1990            104
        The year 1983, for example, is then referred to, relative to the
base year of 1985,              
        as year x=-2.           
Exponential--often used to model growth or decay                        
     Population, radio-carbon dating techniques,                        
     Compound interest problems.                        
Base e arise naturally in calculus and in the compounding process--so,
often employed.                 

Logarithmic--inverse of exponential                     
    Not often used, but might be used when increase might cause slowing of
     as for example--when population of a city increases, area of course
increases, but its rate of                      
     increase may slow, as for example when skyscrapers are introduced.                 
     Any exponential may be viewed as a logarithmic by inverting the role
of dependent                    
     and independent variable.                  

For example, supply and demand analysis traditionally sees price per unit
as a function                   
of quantity per unit of time--
but, in varying situations, one might have, instead of price=f(quantity), 
the alternate of quantity=f(price).
An exponential in the traditional view becomes a logarithmic in the
alternate view.

Logistic--exponential type of growth initially--environmental resistance
puts ceiling on growth.
     When a population gets sufficiently large, factors such as food
supply and overcrowding tend to
     hold down the growth.  Consumption is proportional to the amount

Gompertz--flatter type of logistic--growth modelling.

A few more references--classics in various fields.

N. Keyfitz, Introduction to the Mathematics of Population, Reading, MA,
Addison-Wesley, 1968.

N. T. J. Bailey, The Mathematical Approach to Biology and Medicine, New
York, John Wiley, 1967.

J. I. Shonle, Environmetnal Applications of General Physics, Reading, MA,
Addison-Wesley, 1975.