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]t \ \textgreater \ 6.25[/tex]
B. [tex]-6.25 \ \textless \ t \ \textless \ 6.25[/tex]
C. [tex]t \ \textless \ 6.25[/tex]
D. [tex]0 \leq t \leq 6.25[/tex]

To determine the interval of time for which Jerald is less than 104 feet above the ground, we start with the given height equation:

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

We need to find the value of [tex]$ t $[/tex] for which [tex]$ h < 104 $[/tex]. First, we can set up the equation:

[tex]\[ -16t^2 + 729 = 104 \][/tex]

We solve for [tex]$ t $[/tex]:

1. Subtract 104 from both sides of the equation:
[tex]\[ -16t^2 + 729 - 104 = 0 \][/tex]
[tex]\[ -16t^2 + 625 = 0 \][/tex]

2. Simplify the equation:
[tex]\[ -16t^2 = -625 \][/tex]

3. Divide both sides by -16:
[tex]\[ t^2 = \frac{625}{16} \][/tex]

4. Take the square root of both sides to solve for [tex]$ t $[/tex]:
[tex]\[ t = \pm \sqrt{\frac{625}{16}} \][/tex]
[tex]\[ t = \pm \frac{25}{4} \][/tex]
[tex]\[ t = \pm 6.25 \][/tex]

Thus, we have [tex]$ t = 6.25 $[/tex] and [tex]$ t = -6.25 $[/tex].

However, since [tex]$ t $[/tex] represents time in seconds and cannot be negative, we only consider the positive value: [tex]$ t = 6.25 $[/tex].

Therefore, the interval of time for which Jerald's height is less than 104 feet above the ground is:

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

So, the correct answer is:

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