A town in the mid west has been experiencing a steady population decline of 1.5 % per year for the past decade.

Question

If there were 31050 residents in the year 2011 and the trend continues, what will the population be in the year 2029?

 

I can not think of a formula that is working to give me the answer for this. 

Answer 1

If it drops by 1.5% each year, then at the end of a particular year, the population is 0.985 times what it was at the start of the year.  Keep this up for t years and you get

 

P(t) = P₀ (0.985)^t

 

where t = number of years elapsed from when the population was P₀.

 

Year 2029:

 

t = 2029 - 2011 = 18 years

 

P₀ = 31050

 

P(18) = 31050 (0.985)¹⁸ = 23654

Answer 2

P = P₀(.985)^x

 

This should work to give you the answer you are looking for. P₀ is the initial population. X is the number of years that have passed since 2011.

 

2029-2011 = 18

 

P = 31050 (.985)¹⁸