Assume real per capita GDP in West Springfield is $10,000 while in East Vice City it is $2,500. The annual growth rate in West Springfield is 2.33%, while in East Vice City it is 7%. How many years will it take for East Vice City to catch up to the real per capita GDP of West Springfield?

31 year will be taken

Explanation:

given data

real per capita GDP P1 = $10,000

East Vice City P2 = $2,500

annual growth rate r1 = 2.33%

East Vice City r2 = 7%

solution

we get here no of time period in year that is express here as

    ........................1

put here value and we will get

10000 ×   =  2500 ×    

take ln both side we get

ln ( ) = t × ln ( \frac{1.07}{1.0233} )

1.386294 =  t × 0.04462

t = 31.068

time = 31 year

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