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]

To solve the problem of finding the time interval when Jerald is less than 104 feet above the ground, we'll use the given height formula:

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

We want his height, [tex]\( h \)[/tex], to be less than 104 feet:

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

Now, let's solve the inequality step-by-step:

1. Rearrange the inequality:

Subtract 104 from both sides:

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

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

[tex]\[ -16t^2 < -625 \][/tex]

2. Divide by -16:

Remember, when dividing by a negative number, the inequality sign flips:

[tex]\[ t^2 > \frac{625}{16} \][/tex]

3. Calculate the critical points:

Find the square root of both sides:

[tex]\[ t > \frac{25}{4} \][/tex]

[tex]\[ t > 6.25 \text{ or } t < -6.25 \][/tex]

Since time [tex]\( t \)[/tex] cannot be negative in this context (because Jerald cannot jump back in time), we only consider [tex]\( t > 6.25 \)[/tex].

4. Conclusion:

Jerald’s height will be less than 104 feet when [tex]\( t > 6.25 \)[/tex].

Therefore, the correct interval of time during which Jerald is less than 104 feet above the ground is:

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