Answer
Graph of $S(x)=100\log_2(x+2)$
Work Step by Step
Substituting values of $x$ in the given function, $
S(x)=100\log_2(x+2)
$, results to
\begin{array}{c|c|c}
\text{If }x=0: & \text{If }x=2 & \text{If }x=6
\\\\
S(x)=y=100\log_2(x+2) & S(x)=y=100\log_2(x+2) & S(x)=y=100\log_2(x+2)
\\
y=100\log_2(0+2) & y=100\log_2(2+2) & y=100\log_2(6+2)
\\
y=100\log_2 2 & y=100\log_2 4 & y=100\log_2 8
\\
y=100(1) & y=100\log_2 2^2 & y=100\log_2 2^3
\\
y=100 & y=100\cdot2\log_2 2 & y=100\cdot3\log_2 2
\\
& y=100\cdot2(1) & y=100\cdot3(1)
\\
& y=200 & y=300
.\end{array}
Tabulating the results above gives the table below.
\begin{array}{c|c}
\hline
x & y
\\\hline
0 & 100
\\\hline
2 & 200
\\\hline
6 & 300
\end{array}
Connecting the points $
\left(0,100\right),
\left(2,200\right),
\text{ and }
\left(6,300\right)
$ with a curve gives the graph of $
S(x)=100\log_2(x+2)
$.
