Help with Differential Equation

[blurain]

Hi, I really need help with this differential equation that I am currently solving:

a) Translate "the level of water in a tank decreases at a rate equal to one-tenth the square root of the level of water in the tank" into an equation.

b) Sketch a graph which could represent the level of water in the tank from t=0 to t=10. Be sure to label the axes. If there are many possible graphs, sketch three examples.

So far, I translated the equation into W'(t)= -.1 times the square root of W. I don't know if this is correct, and if it is, I don't know how to put it into a graph. Please help. Thank you.

 

[tkhunny]

a) Translate "the level of water in a tank decreases at a rate equal to one-tenth the square root of the level of water in the tank" into an equation.

It doesn't look like you're solving it.

L is the level in the tank.

dL is the change in the tank level.

\(\displaystyle dL = k\frac{1}{10}\sqrt{L}\)

Figure out what 'k' is. It's important. What is its sign? Also important.

 

[skeeter]

"the level of water in a tank decreases at a rate equal to one-tenth the square root of the level of water in the tank" ...

I translated the equation into W'(t)= -.1 times the square root of W.

if W represents the level of water in the tank, then your differential equation is correct. it might be better to express it as ...

\(\displaystyle \L \frac{dW}{dt} = -.1\sqrt{W}\)

you can now separate variables and solve for W as a function of time if necessary.

the graph of W will be parabolic, starting at some initial level of W and curving down to the t-axis in a concave up fashion ... the curve will intercept the t-axis when the tank is empty.

this problem is an application of Torricelli's law ... for additional info, go to this link and scroll down to example 3.