Reference no: EM132481577

The cost, C, in millions of dollars, of cleaning an oil spill can be modelled by the function C(p) =20/100-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-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 to that using the rate of change function R(p) for p=50

d) Outline the cost of cleaning up the oil spill. Include the following:

i. Graphs of C(p) and R(p)

ii. The total cost to clean up 25%, 50%, and 90% of the oil spill.

iii. The rate of change of the cost at 25%, 50%, and 90% of the oil spill.