SOLUTION: If the world population is now (in 2009) 6.72 billion people and is growing at 1.14%, how long will it take the population to grow to 10 billion people? I always get confused with

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If the world population is now (in 2009) 6.72 billion people and is growing at 1.14%, how long will it take the population to grow to 10 billion people? I always get confused with       Log On


   

Question 205450: If the world population is now (in 2009) 6.72 billion people and is growing at 1.14%, how long will it take the population to grow to 10 billion people? I always get confused with these problems but would to equation to solve the problem look something like 10 billion=6.72(1.14)?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The equation for population growth is
y=A%2Ae%5E%28kt%29, 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.

10=6.72+%2Ae%5E%28.0114t%29

Divide by 6.72,
10%2F6.72=+e%5E%28.0114t%29

Take the ln of each side:
ln%2810%2F6.72%29=+.0114t

Divide both sides by .0114
%28ln%2810%2F6.72%29%29%2F.0114=t
t=34.868 years

Approximately 35 years from 2009 would be about 2044.

Please see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. My entire explanation on logarithms together with videos with me explaining this can be found on this website. If you need help finding anything, send me an Email.

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