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Ethiopia had about 73 million inhabitants in 2006. The population increased by 2.35% per year. Estimate when the population reaches 110 million.

73*1,0235^x = 110

10^x*lg1,0235 = 10^lg110-73

10^x*lg1,0235 = 10^lg37

x*lg1,0235/lg1,0235 = lg37/lg1,0235

x = 36.1504…

2006 + 36 = 2042

 

 

I did something wrong, and I suck at log's.

Could someone please help me out? :D

Guest Apr 14, 2017
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 #1
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Present population=73 million in 2006

Future population =110 million in ??

 

110,000,000 =73,000,000 x 1.0235^n divide both sides by 73,000,000.

1.506849315 =1.0235^n take the log of both sides

n =Log(1.506849315) / Log(1.0235) 

n =~17.65 years.

 

However, for "natural growth" in population of people, animals, plants.....etc., it is more accurate to use the natural log(ln, and e);

110 =73 x e^(0.0235n)

1.506849315 =e^(0.0235n) take the natural logs of both sides

n =17.45 years - This is slighly more accurate.

Guest Apr 14, 2017
 #2
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Thanks :)

Guest Apr 14, 2017
edited by Guest  Apr 14, 2017
 #3
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Let's go from here :

 

110  =  73(1.0235)^x     divide both sides by 73

 

110/ 73   = (1.0235)^x      take the log of both sides

 

log (110 / 73)  =  log (1.0235)^x

 

And, by a log property,   log(a)^x  =   x *log(a)...so.....the right side becomes

 

log (110 / 73)  =  x * log(1.0235)       divide both sides by log(1.0235)

 

log (110 / 73)   / log (1.0235)   =  x  ≈  17.65  years

 

So.....2006 + 17.65   =   2024  [rounded to the closest year ]

 

 

cool cool cool

CPhill  Apr 14, 2017

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