a steady population decline of 2.25% per year for the past decade. 16100 residents 2011the trend continues, the pop be in the year 2031?

Question

A town in the mid west has been experiencing a steady population decline of 2.25 % per year for the past decade. If there were 16100 residents in the year 2011 and the trend continues, what will the population be in the year 2031? Use the appropriate numerical expression to arrive at your response.
Round your answer to the nearest person.

Answer 1

Since the population drops by 2.25% each year, the population at the end of a year is 97.75% of what it was at the start of the year.  This is 0.9775 times as much.  If you keep this up for t years, you get a final population of

 

P(t) = 16,100 (0.9775)^t,

 

with t = number of years since 2011.

 

In 2031,

 

t = 2031 - 2011 = 20

 

P(20) = 16,100 (0.9775)²⁰ = 10,213