Question

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 1

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.

$log(\frac{I}{12})=-0.025x$

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.

$log(\frac{I}{12})=-0.025(24)$

$log(\frac{I}{12})=-0.6$

$\frac{I}{12}=10^{-0.6}$

$\frac{I}{12}=0.2512$

$I=3.0143$

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.

$log(\frac{7}{12})=-0.025x$

$-0.23433=-0.025x$

$0.23433=0.025x$

$x=\frac{0.23433}{0.025}$

$x=9.3732$

Hence, the light intensity will be 7 lumenus at the depth of 9.3732 feet approximately.