Animal population growth

Question

A population of animals is growing exponentially, and an ecologist has made the following table of the population size, in thousands, at the start of the given year.

 

Year                               2007   2008   2009   2010   2011   2012

Population in thousands    5.25  5.51    5.79    6.04    6.38    6.70  

 

Looking over the table, the ecologist realizes that one of the entries for population size is in error. Which entry is it, and what is the correct population size?

Answer 1

Ana,

If a population is growing exponentially, then the observed increase each successive year should be greater than in the prior year.  So just make a table:

 

  year      population    Increase over prior year

=====  =======   ===============

 2007        5.25                N/A

 2008        5.51                0.26

 2009        5.79                0.28

 2010        6.04                0.25     This is the problem year

 2011        6.38                0.34

 2012        6.70                0.32     Depending how you fix earlier #'s, this may also be a data problem.

 

Probably, the correct population size for 2010 is 6.08 showing a 0.29 increase.  Then, 2011 would show a 0.30 increase and 2012 could be left alone.