Question

The intensity,i, of light passing through water can be modelled by the equation I = 10^1-0.13x, where x is the depth of water in metres. Most aquatic plants require a light intensity of 4.2 units for strong growth. Determine the depth of water at which most aquatic plants recieve the required light.
PLEASE HELP!

Answer 1

I=10^(1-0.13x)
When I=4.2, then:
4.2=10^(1-0.13x)
ln 4.2=ln(10^(1-0.13x))
ln 4.2=(1-0.13x)ln (10)
1-0.13x=ln 4.2 / ln 10
-0.13 x=(ln 4.2 /ln 10)-1
x=[(ln 4.2/ ln 10)-1] /(-0.13)
x=-0.37675/(-0.13)
x=2.898...≈2.9

Answer: The depth of water at which most aquatic plansts recieve the requred light would be 2.9 m