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]

Sure, let's solve the problem step-by-step.

We are given the equation for Jerald's height as a function of time:
[tex]\[ h = -16t^2 + 729 \][/tex]
where [tex]\( h \)[/tex] is the height in feet, and [tex]\( t \)[/tex] is the time in seconds.

We need to determine when Jerald's height is less than 104 feet, according to the options provided.

1. Set up the inequality:
We want to find when [tex]\( h < 104 \)[/tex].

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

2. Solve the inequality:

First, subtract 104 from both sides:

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

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

Now, let's isolate [tex]\( t^2 \)[/tex]:

Subtract 625 from both sides:

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

Divide both sides by -16 (when dividing by a negative number, the inequality sign reverses):

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

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

3. Find the values of [tex]\( t \)[/tex]:

Take the square root of both sides to solve for [tex]\( t \)[/tex]:

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

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

4. Conclusion:

Jerald is less than 104 feet above the ground when [tex]\( t > 6.25 \)[/tex] seconds.

Based on the options provided, the correct interval is [tex]\( t > 6.25 \)[/tex].