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 the interval where Jerald is less than 104 feet above the ground, we start with the equation that models his height:

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

We need to determine the values of [tex]$ t $[/tex] for which [tex]$ h < 104 $[/tex].

1. Set Up the Inequality:
[tex]\[
-16t^2 + 729 < 104
\][/tex]

2. Simplify the Inequality:
Subtract 729 from both sides:
[tex]\[
-16t^2 < 104 - 729
\][/tex]
[tex]\[
-16t^2 < -625
\][/tex]

3. Solve for [tex]$ t^2 $[/tex]:
Divide both sides by -16, remembering to reverse the inequality sign because we're dividing by a negative number:
[tex]\[
t^2 > \frac{-625}{-16}
\][/tex]
[tex]\[
t^2 > 39.0625
\][/tex]

4. Find the Square Root to Solve for [tex]$ t $[/tex]:
Take the square root of both sides:
[tex]\[
t > \sqrt{39.0625} \quad \text{or} \quad t < -\sqrt{39.0625}
\][/tex]
[tex]\[
t > 6.25 \quad \text{or} \quad t < -6.25
\][/tex]

Since time [tex]$ t $[/tex] can't be negative in this context (as it represents time after the jump), we discard the negative possibility:

5. Determine the Time Interval:
Therefore, Jerald's height is less than 104 feet when:
[tex]\[
t > 6.25
\][/tex]

This means Jerald will be less than 104 feet above the ground after 6.25 seconds. The correct interval of time from the given options is:

[tex]$ t > 6.25 $[/tex]