In these problems you are asked to find a function that models a real-life situations....

The model we want is a function that gives the radius of the circle.
For the circle,
${\displaystyle Area=\pi {\left(radius\right)}^2}$
Ler R and A be the radius and area of the circle respectively. Then, we have
${\displaystyle A=\pi R^2}$
There is one varying quantity, which is the area A of the circle.
Because the function we want depends on its area A. then, we must express the radius R in terms of its area A.
Consider, ${\displaystyle A=\pi R^2}$
Divide by ${\displaystyle \pi }$,
${\displaystyle \frac{A}{\pi }=R^2}$
Taking the square root on both sides,
${\displaystyle \sqrt{\frac{A}{\pi }}=\sqrt{R^2}}$
${\displaystyle =R}$
Thus, ${\displaystyle R=\sqrt{\frac{A}{\pi }}}$
Therefore, the model is the function R that gives the radius of the circle in terms of area A is given by,
${\displaystyle R\left(A\right)=\sqrt{\frac{A}{\pi }},A>0}$
Thus, the radius of the circle modeled by the function ${\displaystyle R\left(A\right)=\sqrt{\frac{A}{\pi }},A>0}$.
FInal statement:
The radius of the circle modeled by the function ${\displaystyle R\left(A\right)=\sqrt{\frac{A}{\pi }},A>0}$.