If the population is tripled in 30 years, what is the annual growth rate?
回答 (5)
2017-06-07 1:00 am
✔ 最佳答案
Let x% be the annual growth rate.Let a be the original population.
The population in 30 years.
a (1 + x%)^30 = 3 a
(1 + x%)^30 = 3
log[(1 + x%)^30] = log(3)
30 log(1 + x%) = log(3)
log(1 + x%) = (1/30) log(3)
1 + x% = 10^[(1/30) log(3)]
x% = 10^[(1/30) log(3)] - 1
x% = 0.0373
x = 3.73
The annual growth rate = 3.73%
2017-06-07 12:48 am
To get the percentage, use 100 * (3^(1/30) - 1)
2017-06-07 12:56 am
3 = e^(30 k) ===> k = (1/30) ln 3 ≈ 3.66%
2017-06-07 12:53 am
3 = 1(1 + x)^30
3 = (1 + x)^30
ln(3) = 30(ln(1+x))
ln(1 + x) = ln(3) / 30
(1 + x) = e^(ln(3) / 30)
1 + x = 1.0373
x = 0.0373, or about 3.73 percent.
3 = (1 + x)^30
ln(3) = 30(ln(1+x))
ln(1 + x) = ln(3) / 30
(1 + x) = e^(ln(3) / 30)
1 + x = 1.0373
x = 0.0373, or about 3.73 percent.
2017-06-07 12:48 am
ask a scientist
收錄日期: 2021-04-18 16:58:10
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170606164751AApHNSF