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 determine the interval of time for which Jerald is less than 104 feet above the ground, we start with the given height equation:

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

We want to find when Jerald's height is less than 104 feet, so we set up the inequality:

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

Now, let's solve this inequality step by step:

1. Subtract 104 from both sides of the inequality:
[tex]\[
-16t^2 + 729 - 104 < 0
\][/tex]
Simplifying gives:
[tex]\[
-16t^2 + 625 < 0
\][/tex]

2. Rearrange the inequality:
[tex]\[
-16t^2 < -625
\][/tex]

3. Divide both sides by -16: Remember that dividing by a negative number reverses the inequality sign.
[tex]\[
t^2 > \frac{625}{16}
\][/tex]

4. Take the square root of both sides:
[tex]\[
t > \sqrt{\frac{625}{16}}
\][/tex]

5. Calculate the square root of [tex]$\frac{625}{16}$[/tex]:
[tex]\[
t > \frac{\sqrt{625}}{\sqrt{16}} = \frac{25}{4} = 6.25
\][/tex]

So, Jerald is less than 104 feet above the ground in the interval when:
[tex]\[ 0 \leq t \leq 6.25 \][/tex]

Thus, Jerald's height is less than 104 feet during the time interval from 0 seconds to 6.25 seconds. The correct answer is:

[tex]\[ 0 \leq t \leq 6.25 \][/tex]