Jerald jumped from a bungee tower. If 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]0 \leq t \leq 6.25[/tex]
B. [tex]-6.25 \ \textless \ t \ \textless \ 6.25[/tex]
C. [tex]t \ \textless \ 6.25[/tex]
D. [tex]t \ \textgreater \ 6.25[/tex]

We start with the height equation

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

and we are given that Jerald is less than 104 feet above the ground, so we set up the inequality

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

### Step 1. Isolate the quadratic term

Subtract 104 from both sides:

[tex]$$
-16t^2 + 729 - 104 < 0.
$$[/tex]

Simplify:

[tex]$$
-16t^2 + 625 < 0.
$$[/tex]

### Step 2. Solve the related equation

Set the expression equal to zero to find the boundary values:

[tex]$$
-16t^2 + 625 = 0.
$$[/tex]

Add [tex]$16t^2$[/tex] to both sides:

[tex]$$
625 = 16t^2.
$$[/tex]

Divide both sides by 16:

[tex]$$
t^2 = \frac{625}{16}.
$$[/tex]

Taking the square root of both sides gives:

[tex]$$
t = \pm \frac{25}{4}.
$$[/tex]

Since [tex]$\frac{25}{4} = 6.25$[/tex], we have the critical points

[tex]$$
t = -6.25 \quad \text{and} \quad t = 6.25.
$$[/tex]

### Step 3. Analyze the inequality

The inequality

[tex]$$
-16t^2 + 625 < 0
$$[/tex]

holds for values of [tex]$t$[/tex] that are either less than [tex]$-6.25$[/tex] or greater than [tex]$6.25$[/tex]. Since time [tex]$t$[/tex] cannot be negative, we discard [tex]$t < -6.25$[/tex].

### Final Answer

Taking into account that time starts at 0, the height is less than 104 feet when

[tex]$$
t > 6.25.
$$[/tex]

Thus, Jerald is less than 104 feet above the ground for all times [tex]$t$[/tex] satisfying

[tex]$$
\boxed{t > 6.25.}
$$[/tex]