The light intensity I​ (in lumens) at a depth of x feet in Lake Elizabeth is given by the formula log (StartFraction Upper I Over 12 EndFraction )equals negative 0.025 x . a. Find the light intensity at a depth of 24 feet. b. At what depth is the light intensity 7 ​lumens?

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 ​lumensSubstitute 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.