Problem #$8$: The updating function for the discrete$-$time dynamical system $m_{t+1}=f(m_t)$ is given below.

Consider the following statements.

$($i$)$ The solution starting at $m_0=0\mathrm{.}5$ is decreasing.

$($ii$)m^{**}=0$ is an unstable equilibrium.

$($iii$)$ The solution starting at $m_0=1\mathrm{.}25$ is increasing.

$($iv$)$ The non$-$zero equilibrium is stable.

Determine which of the above statements are True $(1)$ or False $(2).$

So$,$ for example, if you think that the answers, in the above order, are True,False,False, True then you would enter $\text{'}1,2,2,1\text{'}$ into the answer box below $($without the quotes$).$

Problem #$8$:

Submit Problem #$8$ for Grading

$\backslash$table$[[\backslash$table$[[$Problem #$8],[$Your Answer:$],[$Your Mark:$]],$Attempt #$1,$Attempt #$2,$Attempt #$3,$Attempt #$4]]$