anonymous
  • anonymous
A country's population in 1990 was 156 million. In 1996 it was 162 million. Estimate the population in 2016 using the exponential growth formula. Round your answer to the nearest million.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
\[162 = 156(1+x)^{6}\]

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anonymous
  • anonymous
So you need to solve for x first
aric200
  • aric200
I just checked this, It seems correct http://openstudy.com/study#/updates/5201dbfbe4b0ebbcb9c6b14d @wolf1728 The population increases156,000,000 to 162,000,000 over 6 years 156,000,000 * (1+r)^6 = 162,000,000 (1+r)^6 = 162,000,000 / 156,000,000 (1+r)^6 = 1.03846153846154 6 * log(1+r) = log(1.03846153846154) log(1+r) = 0.01639041618817 / 6 log(1+r) = 0.0027317360313616 1+r = 1.0063098786004 r = .0063098786004 Testing the value of r 156,000,000 * (1+ .0063098786004)^6 = 1996 population 156,000,000 * 1.03846153846154 = 162,000,000 1996 population r = .0063098786004 Plug r in to find pop in 2016.
anonymous
  • anonymous
how do I solve for x
anonymous
  • anonymous
\[\frac{ 162 }{ 156 } = (1+x)^6\]
anonymous
  • anonymous
26?
anonymous
  • anonymous
\[1.038461538 = (1+x)^6\] \[1.038461538 - 1 =0.38461538\] \[\sqrt[6]{0.038461538} = 0.0063\]
anonymous
  • anonymous
could u plz just tell me the answer bc I don't get it
anonymous
  • anonymous
183.717165048
anonymous
  • anonymous
that's the answer?
anonymous
  • anonymous
yup
anonymous
  • anonymous
\[2016-1990=26\] \[156(1+0.0063098786004)^{26} = 183.717165048\]
hwyl
  • hwyl
stop giving out answers. cheating will not be tolerated
wolf1728
  • wolf1728
To solve for x you need to tale logs of both sides 162/156=(1+x)^6
wolf1728
  • wolf1728
TAKE logs
wolf1728
  • wolf1728
I guess jherbo isn't here anymore

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