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A chemical processing plant must monitor a certain liquid substance in a batch of product they make. The substance is transferred from one tank into another in the manufacturing process and the rate of flow must be tracked. The function h(x) = 20(0.75)^x describes the height of the liquid in feet still remaining in the tank t minutes after the exit valve was tripped. a. Using the equation above, find the average rate of change in the height for the first 3 minutes. b. Estimate the instantaneous rate of change in the height at 5 minutes and illustrate this value on a graph. c. Interpret your answer to part b. within the context of the problem.

A chemical processing plant must monitor a certain liquid substance in a batch of product they make. The substance is transferred from one tank into another in the manufacturing process and the rate of flow must be tracked. The function h(x) = 20(0.75)^x describes the height of the liquid in feet still remaining in the tank t minutes after the exit valve was tripped. a. Using the equation above, find the average rate of change in the height for the first 3 minutes. b. Estimate the instantaneous rate of change in the height at 5 minutes and illustrate this value on a graph. c. Interpret your answer to part b. within the context of the problem.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A chemical processing plant must monitor a certain liquid substance in a batch of product they make. The substance is transferred from one tank into another in the manufacturing process and the rate of flow must be tracked. The function h(x) = 20(0.75)^x describes the height of the liquid in feet still remaining in the tank t minutes after the exit valve was tripped. a. Using the equation above, find the average rate of change in the height for the first 3 minutes. b. Estimate the instantaneous rate of change in the height at 5 minutes and illustrate this value on a graph. c. Interpret your answer to part b. within the context of the problem.
Transcribed Image Text:A chemical processing plant must monitor a certain liquid substance in a batch of product they make. The substance is transferred from one tank into another in the manufacturing process and the rate of flow must be tracked. The function h(x) = 20(0.75)^x describes the height of the liquid in feet still remaining in the tank t minutes after the exit valve was tripped. a. Using the equation above, find the average rate of change in the height for the first 3 minutes. b. Estimate the instantaneous rate of change in the height at 5 minutes and illustrate this value on a graph. c. Interpret your answer to part b. within the context of the problem.
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