+0

# I suck at Log's

0
125
3

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.

Guest Apr 14, 2017
Sort:

#1
0

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
0

Thanks :)

Guest Apr 14, 2017
edited by Guest  Apr 14, 2017
#3
+76976
+1

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 ]

CPhill  Apr 14, 2017

### 30 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details