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]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]

We start with the height function given by

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

We want to find the time when Jerald’s height is less than 104 feet. First, we determine the boundary by setting

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

Subtract 104 from both sides to rearrange the equation:

[tex]$$
-16t^2 = 104 - 729 = -625.
$$[/tex]

Next, multiply both sides of the equation by [tex]$-1$[/tex]:

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

Now, divide by 16:

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

Taking the square root of both sides, we find

[tex]$$
t = \sqrt{\frac{625}{16}} = 6.25.
$$[/tex]

Since time cannot be negative, we only consider the positive value [tex]$t = 6.25$[/tex].

The equation [tex]$h(t) = -16t^2 + 729$[/tex] represents a downward-opening parabola, which means that as [tex]$t$[/tex] increases beyond 6.25, the height [tex]$h(t)$[/tex] decreases further. Therefore, Jerald is below 104 feet for all times greater than 6.25 seconds.

Thus, the interval for which he is less than 104 feet above the ground is

[tex]$$
t > 6.25 \quad \text{seconds}.
$$[/tex]