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, we need to find the time interval during which Jerald is less than 104 feet above the ground. The equation modeling his height is [tex]$ h = -16t^2 + 729 $[/tex].

We need to solve the inequality:
[tex]\[ -16t^2 + 729 < 104 \][/tex]

Step-by-step solution:

1. Rearrange the inequality:
Start by subtracting 104 from both sides:
[tex]\[
-16t^2 + 729 < 104
\][/tex]
This simplifies to:
[tex]\[
-16t^2 < 104 - 729
\][/tex]

2. Simplify further:
[tex]\[
-16t^2 < -625
\][/tex]

3. Divide by [tex]$-16$[/tex], and remember to reverse the inequality sign:
When you divide by a negative number, you need to reverse the inequality. So it becomes:
[tex]\[
t^2 > \frac{625}{16}
\][/tex]

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

5. Calculate the square root:
[tex]\[
\sqrt{\frac{625}{16}} = \frac{\sqrt{625}}{\sqrt{16}} = \frac{25}{4} = 6.25
\][/tex]

6. Determine the interval for [tex]$ t $[/tex]:
If [tex]$ |t| > 6.25 $[/tex], this means:
[tex]\[
t < -6.25 \quad \text{or} \quad t > 6.25
\][/tex]

Since time can't be negative in this physical context (Jerald jumping from a tower), we only consider the positive interval:
[tex]\[ t > 6.25 \][/tex]

Therefore, the interval of time for which Jerald is less than 104 feet above the ground is:
[tex]\[ t > 6.25 \][/tex]

Thus, the correct answer is:
[tex]\[ t > 6.25 \][/tex]