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 > 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 solve the problem of finding when Jerald is less than 104 feet above the ground, you can follow these steps:

1. Understand the Given Equation:
Jerald's height is modeled by the equation [tex]$ h = -16t^2 + 729 $[/tex], where [tex]$ h $[/tex] is the height in feet and [tex]$ t $[/tex] is the time in seconds.

2. Set Up the Inequality:
We need to find when his height is less than 104 feet. So, we set up the inequality:
[tex]\[
-16t^2 + 729 < 104
\][/tex]

3. Solve for [tex]$ t $[/tex]:
Start by isolating the term with [tex]$ t $[/tex]:
[tex]\[
-16t^2 < 104 - 729
\][/tex]
[tex]\[
-16t^2 < -625
\][/tex]

4. Simplify the Inequality:
Divide both sides by -16, keeping in mind that dividing by a negative number reverses the inequality sign:
[tex]\[
t^2 > \frac{625}{16}
\][/tex]

5. Solve for [tex]$ t $[/tex]:
Take the square root of both sides:
[tex]\[
t > \frac{25}{4}
\][/tex]
[tex]\[
t > 6.25
\][/tex]

6. Interpret the Result:
Jerald will be less than 104 feet above the ground when the time [tex]$ t $[/tex] is greater than 6.25 seconds.

From the given options, the interval that matches is:
- [tex]$ t > 6.25 $[/tex]

This means that Jerald's height will be less than 104 feet after 6.25 seconds.