How would I calculate population decay?

Question

In a small town named Winchester, the population today is 6722 . For the last five years, the population has declined by 8% every year. If the decline stay the same, what is the expected population in Winchester 8 years from today?

Answer 1

Let P(t) = population in t years from today

P(t) = 6722(1 - 0.08)^t

P(8) = 6722(0.92)⁸ ≈ 3450

Answer 2

P= Po(e^rt) where Po = original Population,

r=annual rate of change=-8%=-.08, t=years=8

P = 6722e^-.08(8)

= 6722/e^.64

use a calculator

= about 3544.46...

= about 3,544 in 8 years at continued 8% decline in population

population tends to grow or decline "naturally" continually so using

continuous compounding instead of annual compounding is more accurate

P=Poe^rt rather than P=(1-r)^t would be more realistic

although both methods are very close in the result

the annual compounding formula might be better, if there's a once a year mating season

but not sure about a once a year dying season, maybe hunting season for lower animals.

or a once a year pandemic for humans or other annual fatal event