Maximum Population of the World
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The current world population as of November 2, 2020 is 7,822,642,000 with an annual growth rate of 1.05%.
A) Assume the world population maintains this annual growth rate, what will the world population be in 10 years? 25 years, 50 years?
B) The total surface area of the Earth is about 5.1 x 10^14 m^2. Taking into account the area needed to grow food and to find other resources, each person needs about 10^4 m^2 of area to survive. According to this, what is the maximum population the earth can sustain?
C) Using the current population and growth rate provided above, calculate how long it will take to reach this population limit on Earth.
First, find Tdouble (it is fine to use the approximate doubling time formula). Tdouble = 70/p, where p is the percent rate of increase/decrease.
Second, put these values into the Doubling time calculations equation:
new value = initial value * 2 ^(t/Tdouble)
Third, solve for t.
There are two ways both using logs to solve for a variable in the exponent:
One Way - Take the log of both sides.
First, get the 2^(t/Tdouble) by itself on one side of the equation.
Then take the log of both sides.
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A)
Use the exponential growth formula
A = P(1 + r)^t
where
P = 7,822,642,000
r = 1.05/100 = 0.0105
t = 10
A = 7,822,642,000 (1 + 0.0105)^10
= 8,683,936,397 (population after 10 years)
Use the exponential growth formula
A = P(1 + r)^t
where
P = 7,822,642,000
r = 1.05/100 = 0.0105
t = 25
A = 7,822,642,000 (1 + ...
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