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]

Sure, let's solve this problem step-by-step to find the interval of time during which Jerald is less than 104 feet above the ground.

Given the height equation:
[tex]\[ h = -16t^2 + 729 \][/tex]

We need to determine when:
[tex]\[ -16t^2 + 729 < 104 \][/tex]

Step 1: Subtract 104 from both sides to form a standard inequality:
[tex]\[ -16t^2 + 729 - 104 < 0 \][/tex]
[tex]\[ -16t^2 + 625 < 0 \][/tex]

Step 2: Simplify and solve for [tex]$ t^2 $[/tex]:
[tex]\[ -16t^2 < -625 \][/tex]
Divide both sides by -16 (note: this reverses the inequality sign):
[tex]\[ t^2 > \frac{625}{16} \][/tex]
[tex]\[ t^2 > 39.0625 \][/tex]

Step 3: Take the square root of both sides:
[tex]\[ t > \sqrt{39.0625} \][/tex]
[tex]\[ t > 6.25 \][/tex]

So, the time [tex]$ t $[/tex] must be greater than 6.25 seconds for Jerald to be less than 104 feet above the ground.

Now, let's match this result to one of the provided intervals:
1. [tex]$ t > 6.25 $[/tex]
2. [tex]$ -6.25 < t < 6.25 $[/tex]
3. [tex]$ t < 6.25 $[/tex]
4. [tex]$ 0 \leq t \leq 6.25 $[/tex]

From our solution, the interval where Jerald is less than 104 feet above the ground is:
[tex]\[ t > 6.25 \][/tex]

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