We are given the following data:
Year
Estimated Population
0 100
1 79
2 62
3 49
4 39
Just by looking at the data we can see that the
relationship of year and estimated population is not linear. The decrease in
the population does not follow a linear path, that is:
79 – 100 is not equal to 62 – 79
-21 is not equal to -17
Therefore, the relationship must be exponential. Let us
find the common ratio by dividing the population in year 1 and year 0:
common ratio, r = 79 / 100 = 0.79
This means that the population decreases by 21% every
year.
So the model for this data can be written as:
yn = y0 * r^n
Where,
yn = is the population after n years
y0 = initial population
r = growth rate = decreasing
n = number of years
