A tank of water is contaminated with 64 pounds of salt. In order to bring the salt concentration down to a level consistent with EPA standards, clean water is being piped into the tank, and the well-mixed overflow is being collected for removal to a toxic-waste site. The result is that at the end of each hour there is 21% less salt in the tank than at the beginning of the hour. Let S = S(t) denote the number of pounds of salt in the tank t hours after the flushing process begins.(a) Explain why S is an exponential function.The amount of salt is being decreased by__________each hour, so the decay is at a___________ rate.Find its hourly decay factor.(b) Give a formula for S.S = (c) Make the graph of S that shows the flushing process during the first 15 hours. Describe in words how the salt removal process progresses. amounts of salt are removed early in the process, and, as time passes, the rate of removal .(d) In order to meet EPA standards, there can be no more than 3 pounds of salt in the tank. How long must the process continue before EPA standards are met? (Round your answer to two decimal places.) hr(e) Suppose this cleanup procedure costs $8000 per hour to operate. How much does it cost to reduce the amount of salt from 64 pounds to 3 pounds? (Round your answer to the nearest dollar.)$ How much does it cost to reduce the amount of salt from 3 pounds to 0.1 pound? (Round your answer to the nearest whole dollar.)

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Answered: A tank of water is contaminated with 64…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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A tank of water is contaminated with 64 pounds of salt. In order to bring the salt concentration down to a level consistent with EPA standards, clean water is being piped into the tank, and the well-mixed overflow is being collected for removal to a toxic-waste site. The result is that at the end of each hour there is 21% less salt in the tank than at the beginning of the hour. Let S = S(t) denote the number of pounds of salt in the tank t hours after the flushing process begins.

(a) Explain why S is an exponential function.

The amount of salt is being decreased by__________each hour, so the decay is at a___________ rate.

Find its hourly decay factor.

(b) Give a formula for S.
S =

Describe in words how the salt removal process progresses.

amounts of salt are removed early in the process, and, as time passes, the rate of removal .

(d) In order to meet EPA standards, there can be no more than 3 pounds of salt in the tank. How long must the process continue before EPA standards are met? (Round your answer to two decimal places.)
hr

(e) Suppose this cleanup procedure costs $8000 per hour to operate. How much does it cost to reduce the amount of salt from 64 pounds to 3 pounds? (Round your answer to the nearest dollar.)
$

How much does it cost to reduce the amount of salt from 3 pounds to 0.1 pound? (Round your answer to the nearest whole dollar.)

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