Pretend the world's population in 1989 was 5 billion and that the projection for 2017 is 7.5 billion.
What annual rate of growth is assumed in this prediction?
Assuming we take the growth to be exponential , ...
5 e^(28r) = 7.5
e^(28r) = 1.5
ln both sides
ln (e^(28r)) = ln1.5
28r = ln 1.5
r = .0145
the rate is 1.45%
check:
5 e^(28*.0145)
= 7.5
To calculate the annual rate of growth, we need to determine the percentage increase in population from 1989 to 2017.
Step 1: Calculate the population growth:
Population growth = Final population - Initial population
Population growth = 7.5 billion - 5 billion
Population growth = 2.5 billion
Step 2: Calculate the percentage increase in population:
Percentage increase = (Population growth / Initial population) * 100
Percentage increase = (2.5 billion / 5 billion) * 100
Percentage increase = 50%
Step 3: Calculate the annual rate of growth:
Annual rate of growth = Percentage increase / Number of years
Annual rate of growth = 50% / 28 years (from 1989 to 2017)
Annual rate of growth = 1.79%
Therefore, the assumed annual rate of growth in this prediction is 1.79%.