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Algebra

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Wk 6
Sec 12.7 #24
World population growth
In 2008 the world population was 6.7 billion and the exponential growth rate was 1.14% per year.
A.Find the exponential growth function
B.Predict the world’s population in 2014
C.When will the world’s population be 8.0 billion?

Could someone help me with this please?

  • Algebra -

    Growth function:
    Assume Y=year, so Y=2008 is year 2008, etc.

    The exponential growth function is
    N(Y)=N(2008)*1.0114^(Y-2008) for Y≥2008
    or
    N(Y)=(6.7*10^9)*1.0114(Y-2008)
    for Y≥2008

    Population at 2014 is therefore
    N(2014)=(6.7*10^9)*1.0114(2014-2008)
    =7.17*10^9

    The population will reach 8 billion when
    N(Y)=8*10^9
    or
    (6.7*10^9)*1.0114(Y-2008) = 8*10^9
    1.0114(Y-2008)=8/6.7
    Take log on each side and solve for Y:
    Y-2008=log(8/6.7)/log(1.0114)=15.6 years
    So by the middle of 2023, the world population will reach 8 billions.

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