Consider the alcohol consumption model

at$+1=$ at $$

$10\mathrm{.}5$at$4\mathrm{.}3+$ at

$+$ d

where d is the constant amount that is consumed every hour.

$($a$)$Consider the following statement.

The term $$

$10\mathrm{.}54\mathrm{.}3+$ at

$$ represents the amount of alcohol removed over the course of one hour.

Determine if the above statement is True $(1)$ or False $(2).$

So$,$ for example, if you think that the above statement is True then you would enter $\text{'}1\text{'}$ into the answer box below $($without the quotes$).$

$($b$)$Find the equilibrium for this system when d $=4\mathrm{.}9.$

$($c$)$This system has a biologically plausible $($i$.$e$.,$ non$-$negative$)$ equilibrium when d is greater than $0$ and less than what number?