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 solve the problem of finding the interval of time during which Jerald is less than 104 feet above the ground, we start with the equation modeling his height:

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

We want to find when his height [tex]\( h \)[/tex] is less than 104 feet:

[tex]\(-16t^2 + 729 < 104\)[/tex]

Let's solve this inequality step by step:

1. Subtract 104 from both sides:
[tex]\(-16t^2 + 729 - 104 < 0\)[/tex]

2. Simplify the left side of the inequality:
[tex]\(-16t^2 + 625 < 0\)[/tex]

3. Move 625 to the other side:
[tex]\(-16t^2 < -625\)[/tex]

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

5. Take the square root of both sides to solve for [tex]\( t \)[/tex]:
[tex]\(|t| > \sqrt{\frac{625}{16}}\)[/tex]
[tex]\(|t| > \frac{25}{4}\)[/tex]

6. Simplify the square root:
[tex]\(|t| > 6.25\)[/tex]

This result means Jerald is less than 104 feet above the ground when the time [tex]\( t \)[/tex] is greater than 6.25 seconds or less than -6.25 seconds.

Since time cannot be negative in this context, we only consider:

[tex]\( t > 6.25 \)[/tex]

Therefore, the correct interval during which Jerald is less than 104 feet above the ground is when [tex]\( t > 6.25 \)[/tex].