Question

Light passing through water loses 30% of its intensity every metre of water depth. At what depth will the light intensity be half of what it is at the surface?

How is it 8.1? I don't know how.

Thanks

Answer 1

It isn't 8.1

1(.7)^x = .5
take log of both sides and use rules of logs
x log .7 = log .5
x = log.5/log.7 = 1.94

check:
after 1 m, int. = .7
after 2 m, int = .7(.7) = .49 , already less than half

my answer of 1.94 m is very reasonable.

Answer 2

Hmm the answer key says 8.1. I got the same answer you did.