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

#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

#3**+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