Task - Ximera

$\newcommand{\arraycolsep}[3]{} \newcommand{\dd}[2][]{\frac{d #1}{d #2}} \newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} \newcommand{\veci}{\vec{\hat{\bf\imath}}} \newcommand{\vecj}{\vec{\hat{\bf\jmath}}} \newcommand{\utan}{\vec{\hat{t}}} \newcommand{\unormal}{\vec{\hat{n}}} \newenvironment{amatrix}[1]{% \begin{bmatrix} }{% \end{bmatrix} }$

$\newenvironment {prompt}{}{} \newcommand {\ungraded }[0]{} \newcommand {\inputGif }[1]{The gif ‘‘#1" would be inserted here when publishing online. } \newcommand {\HyperFirstAtBeginDocument }[0]{\AtBeginDocument }$

A rock is thrown into a lake, creating a circular ripple that travels outward. As the ripple travels, it displaces sediment on the bottom of the pond.

$R(t)$ is the radius of the ripple at $t$ seconds.
$S(t)$ is the volume of displaced sediment at $t$ seconds.
The total displacement is given by $D(t) = S(R(t))$ .

Determine the average rate of change of $D(t)$ with respect to $t$ between $t=1$ and $t=3$ using the data below.


$t$	$R(t)$	$S(t)$

1	2	5

2	4	10

3	6	15

4	8	20

5	10	25

6	12	30

7	14	35

8	16	40

9	18	45

10	20	50

1.5 3 6 10 20