The table below represents the recommended exercise intensity for an aerobic program based on the number of visits since beginning the program.

\begin{tabular}{|c|c|}
\hline
\begin{tabular}{c}
Number \\
of Visits
\end{tabular} & \begin{tabular}{c}
Exercise \\
Intensity
\end{tabular} \\
\hline
1 & [tex]$60\%$[/tex] \\
\hline
2 & [tex]$60\%$[/tex] \\
\hline
3 & [tex]$60\%$[/tex] \\
\hline
4 & [tex]$?$[/tex] \\
\hline
5 & [tex]$?$[/tex] \\
\hline
6 & [tex]$?$[/tex] \\
\hline
\end{tabular}

The program suggests maintaining a consistent intensity for the first 3 visits, gradually increasing intensity over the subsequent 3 visits, followed by a decrease in intensity for the next 3 visits, before repeating the pattern.

Which of the following options represent the possible intensities for Amber's exercise during the fourth, fifth, and sixth visits? Select three options.

A. [tex]$63\%, 63\%, 63\%$[/tex]

B. [tex]$66\%, 69\%, 72\%$[/tex]

C. [tex]$66\%, 62\%, 58\%$[/tex]

D. [tex]$63\%, 65\%, 67\%$[/tex]

E. [tex]$67\%, 72\%, 77\%$[/tex]

To determine the possible exercise intensities for Amber's fourth, fifth, and sixth visits, we start by analyzing the given pattern in the exercise program.

1. For the first three visits, the exercise intensity remains consistent at 60%.
2. The subsequent three visits (fourth, fifth, and sixth) require a gradual increase in intensity.

Given the options for possible intensities:

- $ 63\% , 63\% , 63\% $
- $ 66\% , 69\% , 72\% $
- $ 66\% , 62\% , 58\% $
- $ 63\% , 65\% , 67\% $
- $ 67\% , 72\% , 77\% $

We need to identify which of these sets represent a gradual increase in intensity. Let’s analyze each option:

1. $ 63\% , 63\% , 63\% $:
- All values are the same, meaning there's no increase. This does not fit the requirement for a gradual increase.

2. $ 66\% , 69\% , 72\% $:
- The values increase progressively: 66% to 69% and then 69% to 72%. This is a valid option as it shows a clear gradual increase.

3. $ 66\% , 62\% , 58\% $:
- The values decrease. This does not fit the requirement for a gradual increase.

4. $ 63\% , 65\% , 67\% $:
- The values increase progressively: 63% to 65% and then 65% to 67%. This is a gradual increase and is a valid option.

5. $ 67\% , 72\% , 77\% $:
- The values increase progressively: 67% to 72% and then 72% to 77%. This shows a clear gradual increase and is a valid option.

Therefore, the valid options representing the possible intensities for Amber's fourth, fifth, and sixth visits, while adhering to the requirement of a gradual increase in intensity, are:

- $ 66\% , 69\% , 72\% $
- $ 63\% , 65\% , 67\% $
- $ 67\% , 72\% , 77\% $

Conclusively, the possible intensities for Amber's exercise during the fourth, fifth, and sixth visits are:

1. $ 66\% , 69\% , 72\% $
2. $ 63\% , 65\% , 67\% $
3. [tex]$ 67\% , 72\% , 77\% $[/tex]