Answer
$\color{blue}{\bf{(a) (A \text{ }\omicron\text{ } r )(t) =\bf{ 16\pi{t^2} } }}$
$\color{blue}{\bf{(b) \text{Which is the area of the oil slick after t minutes } }}$
$\color{blue}{\bf{(c) 144\pi\text{ ft}^2 }}$
Work Step by Step
The radius $r$ of the circular oil slick in feet after $t$ minutes is modeled by the formula:
$r(t) = 4t$
And the area $A$ of the circle is $\pi{r}^2$ or:
$A(r)=\pi{r}^2$
$\bf{(a) }$ $( A \text{ }\omicron\text{ } r )(t) $
$( A \text{ }\omicron\text{ } r )(t) =\pi{(4t)}^2$
$\color{blue}{( A \text{ }\omicron\text{ } r )(t) =\bf{ 16\pi{t^2} }}$
$\bf{(b) }$ $\color{blue}{\bf{\text{Which is the area of the oil slick after t minutes }}}$
$\bf{(c) }$ The area of the slick after $t=3$ minutes is:
$( A \text{ }\omicron\text{ } r )(3) =16\pi{3^2}$
$16\pi{3^2}$
$16\pi(9)$
$\color{blue}{\bf{144\pi\text{ ft}^2}}$
