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SECTION 4-4 C Rate Graphs

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Graphs of “rates” are common in Calculus. While the horizontal axis in such graphs may stand for many things, it often stands for time. The vertical axis stands for some indicated type of rate (often with respect to time).

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Rate Graphs In “Rate” graphs, a Point on the graph represents a value of the indicated rate at a certain time: ___ per ___, a Slope (derivative) represents a rate of change of that indicated rate: ___ per ___ per ___, time (in hrs after midnight) rate of rainfall in (in/hr) The graph at right models the rate of rainfall in inches per hour from midnight until 6:00 A.M. during a tropical rainstorm.

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Rate Graphs the “Signed Area” between the graph and the horizontal (time) axis represents a definite integral which has “undone” the indicated rate to produce an “accumulated value.” In this context, an integral may be thought of as an accumulator. time (in hrs after midnight) rate of rainfall in (in/hr) The graph at right models the rate of rainfall in inches per hour from midnight until 6:00 A.M. during a tropical rainstorm.

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Rate Graphs 1) Write a complete sentence to explain what Point A on the graph represents. Include numbers and units in your answer. time (in hrs after midnight) rate of rainfall in (in/hr) The graph at right models the rate of rainfall in inches per hour from midnight until 6:00 A.M. during a tropical rainstorm.

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Rate Graphs 2) What is the slope of the graph between Points A and B? 3) Write a complete sentence to explain the meaning of your answer to # 2 time (in hrs after midnight) rate of rainfall in (in/hr) The graph at right models the rate of rainfall in inches per hour from midnight until 6:00 A.M. during a tropical rainstorm.

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Rate Graphs 4) What is the slope of the graph between Points B and C? 5) Write a complete sentence to explain the meaning of your answer to #4. time (in hrs after midnight) rate of rainfall in (in/hr)

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Rate Graphs 6) Find 7) Write a complete sentence to explain the meaning of your answer to #6. time (in hrs after midnight) rate of rainfall in (in/hr)

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Rate Graphs 8) Approximate the value of using geometrical regions. Show computations. 9) Write a complete sentence explaining the meaning of your answer in #8. time (in hrs after midnight) rate of rainfall in (in/hr)

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Accumulated Value 10) A chemical flows into a storage tank at a rate ofliters per minute, where Find the amount of the chemical that flows into the tank during the first 20 minutes.

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Assignment: Worksheet 4 - 4c and Page 294 # 57, 58, 60, 105 and 106

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