A rocket is shot straight up from a 30-foot
rooftop with an initial velocity of 128 feet
per second. The height, h, of the rocket is
given by the equation h = -16t^2+ 128t+ 30,
where t is the time elapsed in seconds and h
is the height in feet.
a. How long will it take the rocket to
return to the ground?
b. The maximum height that the rocket
achieves is 286 feet. At what time does
it reach that height?

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!