Answer
See below:
Work Step by Step
(a)
As \[D\left( x \right)\] is the time in minutes to skin damage whereas \[x\] is the UV index and \[D\left( x \right)=.8{{x}^{2}}-17x+109\] is the average time in which skin damage begins for burn prone people.
So, at \[x=1\]
\[\begin{align}
& D\left( 1 \right)=.8\cdot {{1}^{2}}-17\cdot 1+109 \\
& =.8-17+109 \\
& =92.8
\end{align}\]
\[D\left( 1 \right)=92.8\]Interprets that skin damage will begin for burn prone people after \[92.8\] minutes when sun’s UV index is low at \[x=1\].
As \[x\] represents UV index on \[x\]-axis and \[D\left( x \right)\] represents the time in minutes to skin damage.
So, at \[x=1\], locate the value of \[D\left( x \right)\]by seeing the intersection point where \[x=1\] parallel to \[y\]-axis cut the curve, then that point will give the corresponding value of \[y\].
Thus, the point is \[\left( 1,92.8 \right)\] on the graph.
Hence, \[D\left( 1 \right)=92.8\] interprets that skin damage will begin for burn prone people after \[92.8\] minutes when sun’s UV index is low at \[x=1\] and the point on the graph is,\[\left( 1,92.8 \right)\].
(b)
As \[D\left( x \right)\] is the time in minutes to skin damage whereas \[x\] is the UV index and \[D\left( x \right)=.8{{x}^{2}}-17x+109\] is the average time in which skin damage begins for burn prone people.
So, at \[x=10\]
\[\begin{align}
& D\left( 10 \right)=.8\cdot {{10}^{2}}-17\cdot 10+109 \\
& =80-170+109 \\
& =19
\end{align}\]
The \[D\left( 10 \right)=19\]Interprets that skin damage will begin for burn prone people after \[19\] minutes when sun’s UV index is low at\[x=10\].
As \[x\] represents UV index on \[x\]-axis and \[D\left( x \right)\] represents the time in minutes to skin damage.
So, at \[x=10\],locate the value of \[D\left( x \right)\]by seeing the intersection point where \[x=10\]parallel to \[y\]-axis cut the curve, then that point will give the corresponding value of \[y\]or \[D\left( x \right)\].
Thus, the point is \[\left( 10,19 \right)\] on the graph.
Hence, \[D\left( 10 \right)=19\] interprets that skin damage will begin for burn prone people after \[92.8\] minutes when sun’s UV index is low at \[x=10\] and the point on the graph is,\[\left( 10,19 \right)\].
