1. In the year 1970, the population of the planet Earth was estimated to be 3.5
ID: 2847255 • Letter: 1
Question
1. In the year 1970, the population of the planet Earth was estimated to be 3.5 Billion people and
it was growing at a rate of about 2% per year. When does this simple population model,
assuming population growth is directly proportional to population size,
predict we will reach 10 billion people (by year)?
2. Suppose that there was a major world disaster and only 100 young, healthy
people survived, 50 men and 50 women. It is theorized that the planet can only hold a
population of about 10 Billion people. Use the extended population model using maximal
ability of planetary resources and minimal biological levels (let's say 60 people) and a birth
rate of 2% to determine when, in terms of future years, we will have surpassed even 1 million
people living on the planet again?
Explanation / Answer
1. we have growth proportional to population
so
growth = k*population
in 1970 we hve
dp/dt = k*p
lnp=kt ...wher p is from 3.5 to 3.5*1.02 and t is from 0 to 1
k=ln(1.02*3.5/3.5) =0.02
growth over time t years so that population is 10 billion
dp/dt = 0.02*p
lnp =0.02*t p is from 3.5 to 10
we get
t=50*ln(10/3.5) =52.5 years
so a year of 1970+52.5 = 2022.5 year
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