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 this problem, we need to determine when Jerald's height is less than 104 feet. His height as a function of time [tex]\( t \)[/tex] is given by the equation:

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

We need to find the values of [tex]\( t \)[/tex] for which [tex]\( h(t) < 104 \)[/tex]. Let's set up the inequality:

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

To solve for [tex]\( t \)[/tex], we'll start by isolating the quadratic term:

1. Subtract 104 from both sides to simplify the inequality:

[tex]\[ -16t^2 + 729 - 104 < 0 \][/tex]

[tex]\[ -16t^2 + 625 < 0 \][/tex]

2. Rearrange the terms:

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

3. Divide both sides by -16. Remember, when you divide or multiply an inequality by a negative number, you must reverse the inequality sign:

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

4. Simplify the fraction:

[tex]\[ t^2 > 39.0625 \][/tex]

5. Take the square root of both sides to solve for [tex]\( t \)[/tex]. Since [tex]\( t \)[/tex] represents time and should be non-negative, we only consider the positive root:

[tex]\[ t > \sqrt{39.0625} \][/tex]

6. Calculate the square root:

[tex]\[ t > 6.25 \][/tex]

So, Jerald is less than 104 feet above the ground for the time interval where [tex]\( t > 6.25 \)[/tex].

The correct answer is:

[tex]\( t > 6.25 \)[/tex]