Expert: Abe Mantell - 5/24/2006

Question
Hello, this question shouldn't take up too much of your time. On
a test, my teacher gave this question. "Graph what would be
represented if the following flask would be filled with water.
Assume a steady flow of water entering the flask."  He provides a
graph with the axis labeled. "volume (mL)" and "time (s)" We
were required to draw the line that represented the relation. I'm
not going to tell you which was my answer and which was my
teachers. One answer was a straight line and one wasn't. Which
one is currect? I'm not sure if you need it or not but I will draw
the flask. \        /
                \     /
                 |    |
                 |    |
                /     \
               /_____\  

Answer
Hello Tom,

If water enters at a contant rate, then
1. at first, the height rises faster and faster, until
-- the water level reaches the narrowest part.  Thus,
-- the graph will be increasing, concave up.
2. then, once past the narrowest point, the height rises
-- but at a slower rate.  Hence, the graph will be increasing
-- but concave down.  Thus, there is a point of inflection
-- at the narrowest point.

OK?

Abe