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, I'd be happy to help explain how to solve this problem step-by-step.

We need to determine for which interval of time Jerald's height is less than 104 feet above the ground, given the equation for his height: [tex]$ h = -16t^2 + 729 $[/tex], where [tex]$ t $[/tex] is time in seconds.

Step 1: Set up the inequality.

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

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

Step 2: Solve the inequality.

1. Rearrange the inequality:
[tex]\[
-16t^2 + 729 - 104 < 0
\][/tex]
[tex]\[
-16t^2 + 625 < 0
\][/tex]

2. Simplify and solve for [tex]$ t^2 $[/tex]:
[tex]\[
16t^2 > 625
\][/tex]

3. Divide both sides by 16:
[tex]\[
t^2 > \frac{625}{16}
\][/tex]

4. Take the square root of both sides:
[tex]\[
t > \sqrt{\frac{625}{16}}
\][/tex]
[tex]\[
t > 6.25
\][/tex]

Step 3: Consider the context.

Since time [tex]$ t $[/tex] cannot be negative, the only interval for which Jerald is less than 104 feet above the ground is [tex]$ t > 6.25 $[/tex].

Conclusion:

Jerald's height will be less than 104 feet after [tex]$ t = 6.25 $[/tex] seconds. Therefore, the correct interval is [tex]$ t > 6.25 $[/tex].