Question

The bird population on an island is declining at a rate of 2.2% per year. If the population was 3500 in the year 2009, which is the best prediction of the population in the year 2014

Answer 1

3500 in 2009
3500 (.022) = 77
3500 - 77 = 3423
3423 in 2010
3423 (.022) = 75.31
3423 - 75.31 = 3347.69
3347.69 in 2011
3347.69 (.022) = 73.65
3347.69 - 73.65 = 3274.04
3274.04 in 2012
3274.04 (.022) = 72.03
3274.04 - 72.03 = 3202.01
3202.01 in 2013
3202.01 (.022) = 70.44
3202.01 - 70.44 = 3131.57
3131.57 in 2014

ANSWER : 3131.57
I know there is probably an easier way to do this, I just don't know it. All I did was take off 2.2% (.022) from the new total each year.

Answer 2

Or you can use:

\[P(2014) = 3500 \times (1 - 0.022)^{2014-2009} = 3131.571401\]