Jerald jumped from a bungee tower. The equation that models his height, in feet, is given by [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 \ > \ 6.25[/tex]
B. [tex]-6.25 \ < \ t \ < \ 6.25[/tex]
C. [tex]t \ < \ 6.25[/tex]
D. [tex]0 \leq t \leq 6.25[/tex]

To determine for which interval of time Jerald is less than 104 feet above the ground, we’ll analyze the height equation:

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

We need to find when his height [tex]$ h(t) $[/tex] is less than 104 feet:

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

### Solving the Inequality:

1. Isolate the [tex]$ t^2 $[/tex] term:

Subtract 729 from both sides:
[tex]\[
-16t^2 < 104 - 729
\][/tex]

Simplify the right side:
[tex]\[
-16t^2 < -625
\][/tex]

2. Solve for [tex]$ t^2 $[/tex]:

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

Simplify the division:
[tex]\[
t^2 > 39.0625
\][/tex]

3. Find [tex]$ t $[/tex]:

Take the square root of both sides to solve for [tex]$ t $[/tex]:
[tex]\[
t > \sqrt{39.0625}
\][/tex]

The square root of 39.0625 is approximately 6.25, so:
[tex]\[
t > 6.25
\][/tex]

### Conclusion:

The interval for which Jerald is less than 104 feet above the ground is when [tex]$ t > 6.25 $[/tex]. Therefore, the correct interval is:

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