Answer
Domain = $\{t\in \mathbb{R}\ |\ 0\leq t\leq 624\}$ or $[0,624]$
A better domain would be $\{t\in \mathbb{R}\ |\ 0\leq t\leq 100\}$ or $[0,100]$
(see note in the step-by-step instructions)
Work Step by Step
If a function is used as a model for an application, the problem situation may require restrictions on the domain. For example, length and time are generally nonnegative, and a person's age does not increase indefinitely.
$R(t)=46.8-0.075t \quad$ can be calculated for any real number t,
but the sense of the problem is that we take only a nonnegative amount of time into account.
So, $t\geq 0.$
Also, the value $R(t)$ should not be negative, so we restrict t in terms of
$46.8-0.075t\geq 0$
$46.8\geq 0.075t\qquad $... multiply with $\displaystyle \frac{1}{0.075}$
$624\geq t$
Domain = $\{t\in \mathbb{R}\ |\ 0\leq t\leq 624\}$ or $[0,624]$
$NOTE: $
The record is surely never going to be 0 s,
so it might be a good point for this function if we restrict t to say, 100 (years after 1930.)
A better domain would be $\{t\in \mathbb{R}\ |\ 0\leq t\leq 100\}$ or $[0,100]$,
or similar.
