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 \ \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 determine for which interval of time Jerald is less than 104 feet above the ground, we start with the given equation for his height:

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

We want to find when his height is less than 104 feet, so we'll set up the inequality:

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

Rearrange the inequality to isolate the term with [tex]$ t^2 $[/tex]:

[tex]\[ -16t^2 < 104 - 729 \][/tex]
[tex]\[ -16t^2 < -625 \][/tex]

Next, we divide both sides by -16. Remember that dividing an inequality by a negative number reverses the inequality sign:

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

Now, calculate the value:

[tex]\[ \frac{625}{16} = 39.0625 \][/tex]

So, we have:

[tex]\[ t^2 > 39.0625 \][/tex]

To solve for [tex]$ t $[/tex], take the square root of both sides:

[tex]\[ t > \sqrt{39.0625} \][/tex]
[tex]\[ t < -\sqrt{39.0625} \][/tex]

Calculate the square roots:

[tex]\[ \sqrt{39.0625} = 6.25 \][/tex]

Since [tex]$ t $[/tex] represents time, and time cannot be negative in this context, we only consider the positive value:

The valid interval for [tex]$ t $[/tex] is [tex]$ t > 6.25 $[/tex].

So, Jerald is less than 104 feet above the ground for [tex]$ t > 6.25 $[/tex] seconds.