The population of a city increased from 20000 to 40000 in 8 years. Find the population growth rate of the city.
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2007-02-12 1:28 am
回答 (3)
2007-02-12 1:40 am
✔ 最佳答案
Year 1: popu.=20000x(1+x%)
Y2
popu.=20000x(1+x%)^2
Hence
Y8
popu.=20000x(1+x%)^8=40000
(1+x/100)^8=2
8log(1+x/100)=log2
log(100+x)-2=1/8(log2)
log(100+x)=1/8(log2)+2
x=9.051, to 3 d.p.
2007-02-12 1:38 am
let the population growth rate of the city is r
then
20000(1+r)^8=40000
(1+r)^8=2
8log(1+r)=log2
log(1+r)=log2/8=0.0376
1+r=10^0.0376=1.0905
r=0.0905
the population growth rate of the city is 9.05%
then
20000(1+r)^8=40000
(1+r)^8=2
8log(1+r)=log2
log(1+r)=log2/8=0.0376
1+r=10^0.0376=1.0905
r=0.0905
the population growth rate of the city is 9.05%
2007-02-12 1:37 am
Let x(t) be the size of the population as a function of time
and let k be the growth rate
x(t)=x(0)e^(kt)
40000=20000e^(8k)
e^(8k)=2
8k=ln 2
k=ln 2/8
=0.0866 (corr. to 3 significant figures)
and let k be the growth rate
x(t)=x(0)e^(kt)
40000=20000e^(8k)
e^(8k)=2
8k=ln 2
k=ln 2/8
=0.0866 (corr. to 3 significant figures)
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