The population of the Earth is approximately 6 billion people and is growing at an annual rate of 1.9%. Assuming a Malthusian growth model, find the world population

Question

The population of the Earth is approximately 6 billion people and is growing at an annual rate of 1.9%. Assuming a Malthusian growth model, find the world population in 40 years. (Round your answer to one decimal place.)

Answer 1

Given:

e= 2-.7182818285

r= 1.9/100=.019

t= 40

p(0)= 6

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P(40)= 6*(e)^(0.019*40)= 6*2.138376225= 12.8 Billions people

Answer 2

We can use an exponential growth function to find a solution. To start we are told:

1) The population is: 6 billion

2) The population grows at: 1.9% annually

Part One: Exponential Growth Function

F(x) = x (1+r)ⁿ

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x = initial value (6,000,000,000)

r = growth rate, as a decimal (0.019)

x = number of time intervals (40)

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Part Two: Set Up

F(x) = x (1+r)ⁿ

F(x) = 6,000,000,000 * ( 1 + 0.019 )⁴⁰

Step Three: Solve

F(x) = 6,000,000,000 * ( 1.019 )⁴⁰

F(x) = 6,000,000,000 * 2.123084894

F(x) = 12,738,509,360

If we have a graphing calculator such as the TI-83 or TI-84 you could solve this problem using the exponential regression function under the 'stat' menu. Its requires a bit more calculations, but produces the same equation above.

:-)