# Math/College Algebra

A water trough with triangular ends is 9ft long, 4ft wide, and 2ft deep. Initially the trough is full of water, but due to evaporation, the volumn of the water decreases at a rate proportional to the square root of the volume. Using advanced concepts from math and physics, it can be shown that the volume after t hours is give by:
V(t)= 1/C^2(t + 6C)^2
0 is less than or equal to t and t is less than or equal to 6 X absolute value of C. Where C is a constant.

Sketch by hand the graphs of:
y=V(t) for C=-4, C= -5, and C=-6
and give a brief verbal description of this collection of functions.

I find that when t=0 V=36 for all instances of C, but I cannot figure out where to go beyond that.

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1. I think you mean
V = (t+6c)^2 / c^2
36 is just the volume of the tank, so it better be 36 at t = 0 if the tank starts full.
now for each of the three values of c find values of V for t = 1, 2, 3 etc
For example for c = -4
t = 0, V = 36
t = 1 , V = 529/16 = 33.06
t = 2 , V = 484/16 = 27.13
etc
for c = -5
t = 0, V = 36
t = 1, V = 841/25 = 33.64
etc

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posted by Damon

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