Question

With exponential growth rates we often calculate “doubling times.” Hypothetically, if the world’s human population was growing exponentially and doubling every 60 years, and you were told all the areas suitable for humans would be fully occupied by the year 2100, what year would the world’s human habitats be HALF occupied

Answer 1

population grows by exponential growth rate

doubling time is every 60 years

if initial population is a ( a be some positive number)

P(60)= 2a

P(120)= 4a

and so on

this can be applied in reverse direction also

if P(200)= b (b is some positive number) then P(200-60)=P(140)= b/2 (200-60 implies 60 years before)

P(140-60)=P(80)=(b/2)/2= b/4

the population is fully occupied by 2100. so, it is half of full occupancy 60 years before that

so half capacity =2100-60 =2040

world’s human habitats be HALF occupied by year in 2040