Ex. 3 between the years 2000 and 2010, the population of cleveland, ohio decreased, on
average, by 1.85% per year. in 2010, the population was 396,800. if the population s(t),
continues to shrink by 1.85% per year:
a) what will the population be in 2020? state the function s(t).

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

you already gave the answer

step-by-step explanation: