Expert: Jack Cheng - 12/3/2006

Question
regarding the question on 11/14/06 about the pre-calculus problem, how would you find the domain of the area function?

Answer
Hi Holly,

I am assuming you mean this question:

"The water in a cylindrical tank 4ft in diameter empties through a hole in the bottom. Assuming that the water has a depth of 16ft at time t=0 and empties at the rate of 5ft^3/s, express the depth of the water as a function of time."

I am also assuming you are talking about t when you said the domain of the area function.

Well, t has to start to 0. To find out what the last t is, we have to solve the equation d = (64*pi-5t)/(4*pi) for when d=0. When the depth is less than zero, the equation is no longer valid (you can't have a negative depth). (See the answer again to see how that equation is derived.)

[VIEW WITH FIXED-SIZE FONT LIKE COURIER]

0 = (64*pi-5t)/(4*pi)
0 = (64*pi-5t)
5t = 64*pi
t = (64/5)*pi = 12.8*pi

So the domain is [0, 12.8].

I hope this helps,
Jack