Calculate the equilibrium/stationary state, to two decimal places, of the difference equation x_{t+1}=2x_t+9.1. Round your answer to two decimal places.

Question

BlackTom AI · Accepted Answer

The task is to find the equilibrium (stationary) state x* of the difference equation x_{t+1} = 2 x_t + 9.1.
To locate a steady state, we look for a value x* that remains unchanged from one time step to the next, meaning x_{t+1} = x_t = x*.
Substitute into the equation: x* = 2 x* + 9.1.
Now solve for x*: x* - 2 x* = 9.1, which simplifies to - x* = 9.1, so x* = -9.1.
The problem asks for the equilibrium to two decimal places, so we round -9.1 to -9.10.
Note: There are no answer options provided in the prompt to evaluate, so I cannot comment on which option is correct or incorrect. If options were given, I would assess each one by checking whether it equals -9.10 and explain why any other value does not satisfy the equilibrium condition.

ETF2700 - ETF5970 - S2 2025 Quiz 9

Calculate the equilibrium/stationary state, to two decimal places, of the difference equation x_{t+1}=2x_t+9.1. Round your answer to two decimal places.

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