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Topic: Integral as Accumulator...revisted
Replies: 10   Last Post: Apr 27, 1998 12:36 PM

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 JBrown8250 Posts: 20 Registered: 12/6/04
Re: Integral as Accumulator...revisted
Posted: Apr 27, 1998 12:36 PM

In a message dated 98-04-17 11:58:29 EDT, you write:

<< So on my homework and test, I asked the following kind of
question:

I give a series of graphs (sketches), with descriptions of
quantities on each axis, and numbers on each axis. On each graph I
draw a point on the graph, and I shade in an area beneath a
portion of the graph. The directions are:

For each graph,
(a) say in words what the indicated point tells you (use
specific numbers)
(b) say in words what the indicated area represents, or
say "the area doesn't mean anything."

(Part a is less important than part b; it's there mainly to get
them to think about the meaning of the graph.)

The graphs are sketches of:

(1) x: time (months); y: price of gasoline (\$)
(2) x: time (days); y: daily wombat sales (ferrets/day)
[graph has a bump up during the Christmas shopping season]
(3) x: time (years); y: population of your town (thousands)
(4) x: time (years); y: birth rate (births/year) (thousands)
(5) x: time (days since impregnation); y: cow's daily milk
production (gal/day)
(6) x: time (days); y: the height of a plant (cm)
(7) x: time (days); y: daily sales at a store (\$)
(8) x: time (hours); y: rate of change of temperature (degrees F per min)

(1) (a) after 4 months, the price of gasoline was about \$1.20.
(b) the area doesn't mean anything
(2) (a) on day 10, the store sold about 45 wombats
(b) the area represents the number of wombats sold during
that period of time

Looking at this list of graphs, I see I need some examples with variables
other than time on the x-axis.

------------------------------------------------------------------
Evan Romer Susquehanna Valley HS >>

Thanks for these suggestions. I found them great discussion builders (such as
for suggestion #1, "can you find the average price of gasoline?" "Only if they
sold the same amount of gasoline each day."
As for an example where the x-axis is not time, how about a frequency
distribution?
John Brown
Townsend Harris HS