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