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

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.

Explanation:

Consider the provided formula.

`log((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((I)/(12))=-0.025(24)`

`log((I)/(12))=-0.6`

`(I)/(12)=10^(-0.6)`

`(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((7)/(12))=-0.025x`

`-0.23433=-0.025x`

`0.23433=0.025x`

`x=(0.23433)/(0.025)`

`x=9.3732`

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