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 of finding for which interval of time Jerald is less than 104 feet above the ground, we need to work with the given height equation:

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

We want to find when this height, [tex]$ h $[/tex], is less than 104 feet:

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

Let's solve this inequality step-by-step:

1. Rearrange the inequality:
Subtract 729 from both sides:

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

Simplify the right side:

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

2. Isolate the quadratic term:
Since the inequality is negative, let's divide both sides by -16. Remember, dividing by a negative number reverses the inequality:

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

3. Solve for [tex]$ t $[/tex]:
Now, solve the inequality [tex]$ t^2 > 39.0625 $[/tex].

Take the square root of both sides:

[tex]\[ t > \sqrt{39.0625} \quad \text{or} \quad t < -\sqrt{39.0625} \][/tex]

4. Interpret the solution in terms of time, [tex]$ t $[/tex]:
Since time, [tex]$ t $[/tex], cannot be negative (as we're considering the time after Jerald jumps), we only consider the solution where [tex]$ t $[/tex] is positive:

[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]