Jerald jumped from a bungee tower. 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, we need to determine when Jerald's height is less than 104 feet above the ground. The equation modeling his height is given by:

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

We want to find the interval of time [tex]\( t \)[/tex] when his height [tex]\( h \)[/tex] is less than 104 feet, so we set up the inequality:

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

Let's solve this step-by-step:

1. Subtract 104 from both sides:

[tex]\[ -16t^2 + 729 - 104 < 0 \][/tex]

[tex]\[ -16t^2 + 625 < 0 \][/tex]

2. Rearrange the inequality:

[tex]\[ -16t^2 < -625 \][/tex]

3. Divide both sides by -16. Remember, dividing by a negative reverses the inequality sign:

[tex]\[ t^2 > \frac{625}{16} \][/tex]

4. Simplify the fraction:

[tex]\[ t^2 > 39.0625 \][/tex]

5. Take the square root of both sides:

[tex]\[ t > \sqrt{39.0625} \][/tex]

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

Since Jerald's height must also be less than 104 feet above the ground and time cannot be negative, the valid interval is when [tex]\( t \)[/tex] is greater than 6.25. Therefore, the interval for which Jerald is less than 104 feet above the ground is:

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

Thus, among the given options, [tex]\( t > 6.25 \)[/tex] is the correct choice.