Question 205453
The equation for population growth is 
, where y is the population at any time t, and A is the initial population, and k is the growth constant. In this case, A is the present population in 2009, which is 6.72 billion, and k=1.14%=0.0114. The value of y is 10 billion, and the unknown is the value of t, which is the number of years after 2009 when the population reaches 10 billion. 

 

Divide by 6.72, 
 

Take the ln of each side: 
 

Divide both sides by .0114 

 years 

Approximately 35 years from 2009 would be about 2044. 

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