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
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.
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 ]