Expert: Sherman D. - 12/1/2007

Question
QUESTION: Dear Sir,

One country population becomes exact Double after 23 years so how much percent increase the population every after one year

ANSWER: 2 = e^(23r)
ln(2) = 23r
r = ln(2)/23
r = about 3.014%

---------- FOLLOW-UP ----------

QUESTION: Dear Sir,

    Please explain me about e and ln formulas and how it become ln(2)/3=3.014 please give me some explanations
Thank you so much


Answer
Your talking about a country population's growth, which is usually defined as exponential growth.

the reason for the 2 = e^(23r)

usually if a population doubles, you would end up with 2 = e^(tr), because once you divide the doubled population by the original population, you get 2 on the left side.

so i basically explained the e as being exponential population, and you know the rest.

so

2 = e^(23r)

ln(natural logarithms) is the opposite of exponential, and to get 23r by itself on one side, you have to use inverse operations, so you get ln(2) = 23r, and you know the rest.