# The cost of purifying a gallon of water to a purity of x percent is shown below.C(x) = 100100 − x  cents for 50 ≤ x < 100(a) Find the instantaneous rate of change of the cost with respect to purity.C'(x) = −100(100−x2)​+1100−x​   (b) Evaluate this rate of change for a purity of 95%.C'(95) =  centsInterpret your answer.The cost is  ---Select--- increasing decreasing by this amount per additional percent of purity.(c) Evaluate this rate of change for a purity of 98%.C'(98) =  centsInterpret your answer.The cost is  ---Select--- increasing decreasing by this amount per additional percent of purity.

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The cost of purifying a gallon of water to a purity of x percent is shown below.

C(x) =
 100 100 − x

cents for
50 ≤ x < 100
(a) Find the instantaneous rate of change of the cost with respect to purity.
C'(x) =
−100(100−x2)​+1100−x​

(b) Evaluate this rate of change for a purity of 95%.
C'(95)
=  cents

The cost is  ---Select--- increasing decreasing by this amount per additional percent of purity.

(c) Evaluate this rate of change for a purity of 98%.
C'(98)
=  cents

The cost is  ---Select--- increasing decreasing by this amount per additional percent of purity.
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### Calculus 