Jerald jumped from a bungee tower. If the equation that models his height, in feet, is [tex]h = -16t^2 + 729[/tex], where [tex]t[/tex] is the time in seconds, for which interval of time is he less than 104 feet above the ground?

A. [tex]-6.25 \ \textless \ t \ \textless \ 6.25[/tex]

B. [tex]t \ \textgreater \ 6.25[/tex]

C. [tex]0 \leq t \leq 6.25[/tex]

D. [tex]t \ \textless \ 6.25[/tex]

Sure, let's work through the problem step-by-step to find out for which interval of time Jerald is less than 104 feet above the ground, given his height equation:

[tex]\[ h = -16t^2 + 729 \][/tex]

We need to determine the time [tex]\( t \)[/tex] when [tex]\( h < 104 \)[/tex] feet.

1. Start with the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]

2. Isolate the term involving [tex]\( t \)[/tex]:
[tex]\[ -16t^2 < 104 - 729 \][/tex]

3. Simplify the right side of the inequality:
[tex]\[ -16t^2 < -625 \][/tex]

4. Divide both sides by -16 (note that dividing by a negative number reverses the inequality sign):
[tex]\[ t^2 > \frac{625}{16} \][/tex]

5. Calculate the right side of the inequality:
[tex]\[ t^2 > 39.0625 \][/tex]

6. Take the square root of both sides to solve for [tex]\( t \)[/tex] (both positive and negative roots):
[tex]\[ t > \sqrt{39.0625} \][/tex]
[tex]\[ t > 6.25 \][/tex]

Since we are dealing with the context of time in seconds, a negative time wouldn't make sense for this scenario, so we only consider the positive root.

Therefore, Jerald will be less than 104 feet above the ground for:
[tex]\[ t > 6.25 \][/tex]

So, the correct interval is:
[tex]\[ \boxed{t > 6.25} \][/tex]