6_1_Student_Notes.pdf - Lesson 1 Approximating Areas with...

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Lesson 1: Approximating Areas with Riemann Sums Topic 6.1: Exploring Accumulations of ChangeLet’s take a look at the relationship between the graph of a rate of change functionand the area of the region between that derivative graph and the x-axis. Consider the tropical cyclone Imeldathat brought more than 40 inches of rainfall over a 72-hour period in Southeast Texas during September 2019. EX #1: In order to avoid flood water entering your home, you rent a pump that can remove water at a rate of 500 gallons per hour for the first 8 hours of pumping. As the storm grew stronger, you got a second pump; and, for the next 16 hours you could remove 900 gallons per hour using two pumps.1A. Draw a graph that models the removal of storm water from your property. Label the axes correctly. 1B.When we say “area under a curve”this represents the area between the graph and the horizontal axis. Find the area under the graph from 0 to 8 hours. What does this value represent in context to the tropical storm Imelda1C.Find the total area under the graph for the entire 24-hour period. Explain the meaning in context to the scenario. ?
Finding Area Using Riemann Sums

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