College

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]

Answer :

Let's solve the problem step-by-step to find for which interval of time Jerald is less than 104 feet above the ground.

1. Understand the equation:

The equation given is [tex]\( h = -16t^2 + 729 \)[/tex], where [tex]\( h \)[/tex] is Jerald's height in feet and [tex]\( t \)[/tex] is the time in seconds.

2. Set up the inequality:

We are asked to find when Jerald's height [tex]\( h \)[/tex] is less than 104 feet:
[tex]\[ -16t^2 + 729 < 104 \][/tex]

3. Simplify the inequality:

First, subtract 104 from both sides:
[tex]\[ -16t^2 + 729 - 104 < 0 \][/tex]
[tex]\[ -16t^2 + 625 < 0 \][/tex]

4. Rearrange the inequality:

Now, move the constant to the other side to isolate [tex]\( t^2 \)[/tex]:
[tex]\[ -16t^2 < -625 \][/tex]

Dividing both sides by -16 (remember to reverse the inequality because you are dividing by a negative number):
[tex]\[ t^2 > \frac{625}{16} \][/tex]

5. Solve for [tex]\( t \)[/tex]:

Take the square root of both sides:
[tex]\[ t > \sqrt{\frac{625}{16}} \][/tex]

Calculating the square root:
[tex]\[ t > \frac{25}{4} \][/tex]

Therefore, the critical value where Jerald is less than 104 feet above the ground is:
[tex]\[ t > 6.25 \][/tex]

6. Conclusion:

Jerald is less than 104 feet above the ground when time [tex]\( t \)[/tex] is greater than 6.25 seconds. This corresponds to the interval [tex]\( t > 6.25 \)[/tex].

So, the correct answer is:
[tex]\[ t > 6.25 \][/tex]