# Differential Equations-Application of 1st order differential equations 1

• May 18th 2009, 01:46 AM
sanikui
Differential Equations-Application of 1st order differential equations 1
Sunlight transmitted into water loses intensity as it penetrates to greater depths. The rate at which the intensity decreases with depth is proportional to the intensity at that depth. At a depth of 10 metres, the intensity is 30% of its original intensity at the surface. At what depth would the intensity be 20% of that surface?

What is the differential equation?
• May 18th 2009, 02:23 AM
mr fantastic
Quote:

Originally Posted by sanikui
Sunlight transmitted into water loses intensity as it penetrates to greater depths. The rate at which the intensity decreases with depth is proportional to the intensity at that depth. At a depth of 10 metres, the intensity is 30% of its original intensity at the surface. At what depth would the intensity be 20% of that surface?

What is the differential equation?

Solve $\frac{dI}{dx} = -kI$ subject to the boundary conditions $I(0) = I_0$ and $I(10) = 0.3 I_0$.

Then solve $I(x) = 0.2 I_0$ for $x$.
• May 18th 2009, 03:49 AM
sanikui
OK...