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The cost,
C
, in millions of dollars, of cleaning
up an oil spill can be modelled by the function
C
(
p
)
±
20
__
100
²
p
, where
p
is the percent of
the oil that was spilled. The rate of change
of the cost, in millions of dollars, is given by
R
(
p
)
±
20
__
(100
²
p
)
2
.
a)
State the domain and range of each
function, and explain what they mean.
b)
Calculate the rate of change at
p
±
50,
using the slope of the tangent to
C
(
p
).
c)
Compare the rate of change from part b)
to that using the rate of change function
R
(
p
)
for
p
±
50.
d)
Write a report outlining the cost of cleaning
up the oil spill. Include the following:
•
graphs of
C
(
p
) and
R
(
p
)
•
the total cost to clean up 25%, 50%,
and 90% of the spill
•
the rate of change of the cost at 25%,
50%, and 90% of the spill
50%, and 90% of the spill
