Answer
SHOWN BELOW
Work Step by Step
(a)
The expression as follows:
\[H=\frac{1}{2}\left( 220-a \right)\]
Now, put \[a=30\],as the age and to get the value of expression.
\[\begin{align}
& H=\frac{1}{2}\left( 220-30 \right) \\
& H=\frac{1}{2}\left( 190 \right) \\
& H=1\left( 95 \right) \\
& H=95 \\
\end{align}\]
The lower limit of range is 95 beats per minute.
The lower limit of the heart rate range is 95 beats per minute for the age of 30 years old to improve overall health.
(b)
The expression as follows:
\[H=\frac{3}{5}\left( 220-a \right)\]
Now, put \[a=30\],as the age and to get the value of expression.
\[\begin{align}
& H=\frac{3}{5}(220-30) \\
& H=\frac{3}{5}(190) \\
& H=3(38) \\
& H=114 \\
\end{align}\]
The upper limit of range is 114 beats per minute.
The upper limit of the heart rate range is 114 beats per minute for the age of 30 years old to improve overall health condition.
