Answer:
The light intensity at a depth of 24 feet is 3.0143 lumens.
The light intensity will be 7 lumenus at the depth of 9.3732 feet approximately.
Step-by-step explanation:
Consider the provided formula.
[tex]log(\frac{I}{12})=-0.025x[/tex]
Where I is the intensity of light and x is the depth.
Part (A) Find the light intensity at a depth of 24 feet.
Substitute x=24 in above formula.
[tex]log(\frac{I}{12})=-0.025(24)[/tex]
[tex]log(\frac{I}{12})=-0.6[/tex]
[tex]\frac{I}{12}=10^{-0.6}[/tex]
[tex]\frac{I}{12}=0.2512[/tex]
[tex]I=3.0143[/tex]
Hence, the light intensity at a depth of 24 feet is 3.0143 lumens.
Part (B) At what depth is the light intensity 7 lumens
Substitute I=7 in above formula.
[tex]log(\frac{7}{12})=-0.025x[/tex]
[tex]-0.23433=-0.025x[/tex]
[tex]0.23433=0.025x[/tex]
[tex]x=\frac{0.23433}{0.025}[/tex]
[tex]x=9.3732[/tex]
Hence, the light intensity will be 7 lumenus at the depth of 9.3732 feet approximately.
