Question

Uk's real GDP was 1360 trillion pounds in 2009 and 1434 trillion pounds in 2010.UK's population was 191.5 in 2009 and 193.5 in 2010. The approximate number of years it takes for real GDP per person in UK to double if the 2010 economic growth rate and population growth rate are maintained

Answer 1

Real GDP per person in 2009 was

$$\frac{21360T}{191.5m}$$

and real GDP per person in 2010 was

$$\frac{21434T}{193.5m}$$

The growth rate in real GDP follows a geometric progression with

$$r=\frac{1434T}{193.5m}\times\frac{191.5m}{1360T}=\frac{274611}{263160}$$

We find the value of n that satisfies the equation

$$ar ^{ n−1}=2a$$

$$r ^{n−1}=2$$

$$(\frac{274611}{263160})^{n-1}=2$$ $$n\times\ln\frac{274611}{263160}=ln\frac{549222}{263160}$$

$$n=\frac{ln\frac{549222}{263160}}{ln\frac{274611}{263160}}=17.27yrs$$