Answer:
329,211
S(t) = 396,800 * (1 - 0.0185)^(2020-2010)
Step-by-step explanation:
Lets start by the population of 2010. It was 396,800. If it decreases at a 1.85%, per year it means that un 2011 it had:
396,800 * (1 - 0.0185) = 389,459
If we want that the year 2011 to appear on the equation we can say that
S(2011) = 396,800 * (1 - 0.0185)^(2011-2010) = 389,459
As 2011-2010 = 1
For 2012 it will be the population of 2011 reduced again by 0.0185 (or 1.85%):
S(2011) * (1 - 0.0185) =
Replacing S(2011):
S(2011) * (1 - 0.0185) = 396,800 * [(1 - 0.0185)^(2011-2010)] * (1 - 0.0185)
S(2012) = 396,800 * (1 - 0.0185)^(2012-2010)
If we keep with this sequence we can establish a general formula:
S (t) = 396,800 * (1 - 0.0185)^(t-2010)
Now if we want the population of 2020 just replace t=2020
S(2020) = 396,800 * (1 - 0.0185)^(2020-2010)
S(2020) = 329,211
