Question
Discuss the nature of the following time path:
b) Solve equation: for
Answer :
Word Count : 322
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Skip in 10
The equation given is: [ y_{t+1} - \frac{1}{2}y_t = 6 ] with the initial condition ( y_0 = 1 ). To solve this recursively, we will compute the values of ( y_t ) for different values of ( t ). ### Step 1: Initial Condition We are given that ( y_0 = 1 ). ### Step 2: Solve for ( y_1 ) Substitute ( t = 0 ) into the equation: [ y_{0+1} - \frac{1}{2}y_0 = 6 ] [ y_1 - \frac{1}{2}(1) = 6 ] [ y_1 - \frac{1}{2} = 6 ] [ y_1 = 6 + \frac{1}{2} = 6.5 ] ### Step
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