Questions: 8. Completing the modeling in discrete and continuous variables 1. Consider the discrete model: Xt+1 = aXt + b where a and b are constants. a) Find the fixed point of this system. b) For what values of a is the fixed point stable? c) Suppose a=2 and b=3. Starting with X0 = 0, compute X1, X2, X3, X4, X5. d) Does this sequence converge? If so, to what value? If not, why not?

Transcript text: 8. Completing the modeling in discrete and continuous variables 1. Consider the discrete model: $X_{t+1} = aX_t + b$ where $a$ and $b$ are constants. a) Find the fixed point of this system. b) For what values of $a$ is the fixed point stable? c) Suppose $a=2$ and $b=3$. Starting with $X_0 = 0$, compute $X_1, X_2, X_3, X_4, X_5$. d) Does this sequence converge? If so, to what value? If not, why not?