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Question

Economics Question on Logarithmic Differentiation

The solution of the difference equation xt=12xt−1+3x_t =\frac{1}{2} x_{t-1}+3 is

A

xt=(12)t(x0−6)+6x_t=(\frac{1}{2})^t(x_0-6)+6

B

xt=(12)t(x0−3)−2x_t=(\frac{1}{2})^t(x_0-3)-2

C

xt=(12)t(x0−6)−6x_t=(\frac{1}{2})^t(x_0-6)-6

D

xt=(12)(x0+6)+2x_t=(\frac{1}{2})(x_0+6)+2

Answer

xt=(12)t(x0−6)+6x_t=(\frac{1}{2})^t(x_0-6)+6

Explanation

Solution

The correct answer is (A) : xt=(12)t(x0−6)+6x_t=(\frac{1}{2})^t(x_0-6)+6