13.02.2023

The cia estimates the world population is growing at a rate of 1.167% each year. the world population for 2007 was about 6.6 billion

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11.03.2022, solved by verified expert
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The CIA estimates the world population is growing at a rate of 1.167?% each year. The world population for 2007 was about 6.6 billion. Write an equation for the world population after n years.

Let P be the population at any time t. 

According to the given problem 

dP/dt = (1.167/100)P

dP/P = (1.167/100) dt 

Integrating both sides

logP = (1.167/100)t + C1

P =Ce^[(1.167/100)t]

After n years Put t=n 

P = Ce^[(1.167/100)n]

Where C is a constant value. 

for n = 2007, the value of P = 6.6 billion

6.6 = Ce^[(1.167/100)2007]

6.6 = C e^23.42

C = 6.6/e^23.42 = 14831216154

Therefore 

P = 14831216154 e^[(1.167/100)n]

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