# Exponential growth (easy(?) question):

1. Apr 22, 2013

### beaf123

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. Apr 22, 2013

### jbunniii

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.