Proofs

[Protoman 56]

Wasn't sure if you were feeling up to it so I thought I would just post this and see if you could solve it:

 

1. Under certain conditions the result of the movement of a dissolved substance across a cell's membrane is described by the equation:

 

dy/dt=k(A/V)(c-y)

 

y is the concentration of the suibstance inside the cell, (dy/dt) is the rate at which y changes over time. The letters k, A, V, and c stand for constants, k being the permeability coefficient (a property of the membrane), A the surface area of the membrane, V the cell's volume, and c the concentration of the substance outside the cell. The equation says that the rate at which the concetration changes within the cell is proportional to the difference between it and the outside concentration.

 

With this information you should be able to solve for the equation of y(t) using y0= y(0) (that us supposed to be y at the initial time of 0 is equal to y when the equations variable is substituted with 0).

 

That problem should only take a couple of min, or if u want an easier one you could go for this one:

 

2. The intensity L(x) of feet light x feet beneath the surface of the ocean satisfies the differential equation:

 

d(L)/d(x)=-kL

 

where k is a constant. As a diver you know from experience that diving to 18 feet in the caribbean sea cuts the intensity of the light in half. You cannot work without artificial light when the intensity falls below a tenth of the surface value. About how deep can you expect to work without artificial light.

 

 

The second one is alot easier, for those who want to try it think calculus and use derivatives based along the properties of exponential growth and decay.

 

This equation seems similar to algebra. I'll solve it later, I'm kind of tired from school. Aside from that, I have lots of homework I need to tend to. Hold the thought, and I'll try to solve it asap.

[XGhozt 410]

lol..