Jerald jumped from a bungee tower. The equation that models his height in feet is [tex]h = -1t^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 based on the height equation [tex]$ h = -t^2 + 729 $[/tex], we need to find the values of [tex]$ t $[/tex] where the height [tex]$ h $[/tex] is less than 104 feet.

1. Set up the inequality:
[tex]\[
-t^2 + 729 < 104
\][/tex]

2. Solve for [tex]$ t $[/tex] to find the points where the height is exactly 104 feet:
[tex]\[
-t^2 + 729 = 104
\][/tex]

3. Simplify the equation to isolate [tex]$ t^2 $[/tex]:
[tex]\[
-t^2 + 729 = 104
\][/tex]
[tex]\[
729 - 104 = t^2
\][/tex]
[tex]\[
625 = t^2
\][/tex]

4. Solve for [tex]$ t $[/tex]:
[tex]\[
t^2 = 625
\][/tex]
[tex]\[
t = \pm 25
\][/tex]

So, the values of [tex]$ t $[/tex] are [tex]$ t = -25 $[/tex] and [tex]$ t = 25 $[/tex].

5. Determine the interval where the height is less than 104 feet:
Notice here that the height function [tex]$ h = -t^2 + 729 $[/tex] is a downward-opening parabola. This means that Jerald's height will be greater than or equal to 104 feet when [tex]$ -25 \leq t \leq 25 $[/tex], and it will be less than 104 feet outside this interval.

Therefore, Jerald is less than 104 feet above the ground for the interval:
[tex]\[
t < -25 \quad \text{or} \quad t > 25
\][/tex]

Given the context of the problem (a real-world scenario of time and height), negative values for [tex]$ t $[/tex] generally don't make sense (since [tex]$ t $[/tex] represents time). Thus, we focus on the positive values:

For practical purposes, the interval of time where Jerald is less than 104 feet above the ground is:
[tex]\[
t > 25
\][/tex]