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 of determining when Jerald is less than 104 feet above the ground given the equation [tex]$ h = -16t^2 + 729 $[/tex], we start by setting up the inequality based on the height:

1. Set up the inequality:
We want to find when [tex]$ h < 104 $[/tex]. So, we set up the inequality:
[tex]\[
-16t^2 + 729 < 104
\][/tex]

2. Rearrange the inequality:
Subtract 729 from both sides:
[tex]\[
-16t^2 < 104 - 729
\][/tex]
Simplify the right side:
[tex]\[
-16t^2 < -625
\][/tex]

3. Divide both sides by -16:
Remember, dividing by a negative number will flip the inequality sign:
[tex]\[
t^2 > \frac{625}{16}
\][/tex]

4. Solve for [tex]$ t $[/tex]:
Take the square root of both sides. We consider the positive root, as time cannot be negative:
[tex]\[
t > \sqrt{\frac{625}{16}}
\][/tex]
Calculate [tex]$ \sqrt{\frac{625}{16}} $[/tex]:
[tex]\[
t > 6.25
\][/tex]

5. Determine the interval:
As we calculated, Jerald's height is less than 104 feet when [tex]$ t > 6.25 $[/tex].

From this analysis, the interval during which Jerald is less than 104 feet above the ground is [tex]$ t > 6.25 $[/tex].