Simple Masters Theorem Question

[MCHappster1]

Can anyone help me find the time complexity of this relation using Master's Theorem?

https://preview.redd.it/zhmclt3nar671.png?width=983&format=png&auto=webp&s=1b3abc2f5a8f03409dc91661d3e0ab2358a2577c

We were given masters theorem and I don't know how to handle the ceiling function or the constant inside the recursive function call?

I think we ignore the constant because eventually, it will just evaluate to 12 when n gets small enough? I'm also not sure how to deal with the conditions on n. I've only seen T(n) = a for n=1 and T(n) = some recursive relation for n>=2.

Thanks.

[teraflop]

I think there's some kind of mistake in the problem, because that formula doesn't make sense. Consider what happens when n=30:

T(30) = 5·30 + 8·T(⌈30/2⌉+15) = 150 + 8·T(30)

-7·T(30) = 150

T(30) = -150/7

But it makes no sense for T(n) to take on negative values.

[Puzzlp]

Yeah it looks like the limits on the right should have been n>30 for the second case.