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Exponential growth (easy(?) question):

  1. Apr 22, 2013 #1
    Back to how income differences is explained in neoclassical theory, one can ask the question why GDP/capita is $5200 in Morocco and $35 500 in France. Real GDP per capita has grown at a rate of about 3.5% from 2008– 2012, GDP/capita in France grew in the same period at a rate of 1.1%. (http://data.worldbank.org/indicator/NY.GDP.PCAP.KD.ZG/countries/1W-XQ-EG-SY-IR-SA?display=default)
    If this holds up GDP/ capita in Morocco will be the same as the one in France in X years.

    So I cant find the X:

    I have tried:

    5200e^ln(1.035)t = 35 500e^ln(1.01)t

    But I cant solve it..:-(

    Hope someone can help me!:)
  2. jcsd
  3. Apr 22, 2013 #2


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    The GDP per capita in Morocco after ##n## years will be ##5200(1.035)^n##, and in France it will be ##35500(1.011)^n##. Now set these equal to each other and solve for ##n##:
    $$5200(1.035)^n = 35500(1.011)^n$$
    or equivalently,
    $$\left(\frac{1.035}{1.011}\right)^n = \frac{35500}{5200}$$
    Taking logs of both sides should get you the answer quickly from here.
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