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------------------------------------------------ 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 \ \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, let's solve the problem step-by-step!

We are given Jerald's height from the ground as a function of time in the equation [tex]\( h = -16t^2 + 729 \)[/tex], where [tex]\( t \)[/tex] is the time in seconds. We need to find the interval of time for which Jerald's height is less than 104 feet.

1. Set up the inequality:
[tex]\[
-16t^2 + 729 < 104
\][/tex]

2. Rearrange the inequality:
Subtract 729 from both sides:
[tex]\[
-16t^2 < 104 - 729
\][/tex]
Simplify the right side:
[tex]\[
-16t^2 < -625
\][/tex]

3. Solve for [tex]\( t^2 \)[/tex]:
Divide each side by -16. Remember, dividing by a negative number flips the inequality sign:
[tex]\[
t^2 > \frac{-625}{-16}
\][/tex]
Simplify the division:
[tex]\[
t^2 > 39.0625
\][/tex]

4. Find [tex]\( t \)[/tex]:
To solve for [tex]\( t \)[/tex], take the square root of both sides. The square root of 39.0625 is approximately 6.25:
[tex]\[
t > \sqrt{39.0625}
\][/tex]
[tex]\[
t > 6.25 \text{ or } t < -6.25
\][/tex]

Since time [tex]\( t \)[/tex] must be greater than or equal to 0 (as we cannot have negative time), we only consider the positive solution:
[tex]\[
t > 6.25
\][/tex]

Thus, Jerald is less than 104 feet above the ground when [tex]\( t > 6.25 \)[/tex]. The correct choice that matches our solution is:
[tex]\[
t > 6.25
\][/tex]