Hello, fifthrapiers!
A vase is one foot tall.
Imagine you are filling the vase with water.
Assuming the water pours at a constant rate,
it takes 10 seconds for the vase to be filled. Code:
* *
/ \
/ \
/:::::::::::\
*:::::::::::::*
\:::::::::::/
\:::::::::/
\:::::::/
**
Sketch a graph of the height of the water versus time.
The student provided this response: Code:
h
 *
 / \
 / \
/ \
 +    *   t

According to the student's graph,
the height of the water increases for while
. . then decreases . . . until the vase is empty!
The vase is 12 inches high.
It takes 10 second to fill the vase.
Since the bottom of the vase gets wider,
. . it takes longer to fill the bottom half than the top half.
Let's say, this takes 6 seconds.
The top of the vase gets narrower, so the water level rises faster.
Let's say, the top half takes only 4 seconds to fill.
Then the graph would look something like this: Code:

12 + o
 * :
 * :
 * :
6 + o :
 * : :
 * : :
 * : :
  *      *    *  t
 6 10
