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anonymous

  • one year ago

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.

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  1. anonymous
    • one year ago
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    @saseal

  2. anonymous
    • one year ago
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    @aric200

  3. anonymous
    • one year ago
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    \[162 = 156(1+x)^{6}\]

  4. anonymous
    • one year ago
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    So you need to solve for x first

  5. aric200
    • one year ago
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    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.

  6. anonymous
    • one year ago
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    how do I solve for x

  7. anonymous
    • one year ago
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    \[\frac{ 162 }{ 156 } = (1+x)^6\]

  8. anonymous
    • one year ago
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    26?

  9. anonymous
    • one year ago
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    \[1.038461538 = (1+x)^6\] \[1.038461538 - 1 =0.38461538\] \[\sqrt[6]{0.038461538} = 0.0063\]

  10. anonymous
    • one year ago
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    could u plz just tell me the answer bc I don't get it

  11. anonymous
    • one year ago
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    183.717165048

  12. anonymous
    • one year ago
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    that's the answer?

  13. anonymous
    • one year ago
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    yup

  14. anonymous
    • one year ago
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    \[2016-1990=26\] \[156(1+0.0063098786004)^{26} = 183.717165048\]

  15. hwyl
    • one year ago
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    stop giving out answers. cheating will not be tolerated

  16. wolf1728
    • one year ago
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    To solve for x you need to tale logs of both sides 162/156=(1+x)^6

  17. wolf1728
    • one year ago
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    TAKE logs

  18. wolf1728
    • one year ago
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    I guess jherbo isn't here anymore

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