Question

For every metre below the surface of a fluid, the light intensity is reduced by 5%. At what depth is the light intensity 25% of the light intensity at the surface? (accurate to the nearest metre)

Answer 1

\[1metre=0.05\]
\[?metre=1-0.25\]
\[?metre=0.75\]
Cross multiply with the first line and third.
\[1\times0.75=0.75\]
\[\frac{ 0.75 }{ 0.05 }=15\]
Therefore 15 metres. Not sure if it's correct but if you have the answers, please do tell me if it's right or wrong.

Answer 2

\[I _{d}=I _{s}(1-0.05)^{d}\]
\[I _{d}=intensity\ at\ d\ metres\]
\[I _{s}=intensity\ at\ surface\]
\[d=depth\ (metres)\]
\[\frac{I _{d}}{I _{s}}=0.25=0.95^{d}\]
Taking natural logs of both sides gives:
\[\ln 0.25=d \times \ln 0.95\]
\[d=\frac{\ln 0.25}{\ln 0.95}=you\ can\ calculate\]