MATH 121 Lecture Notes - Lecture 3: Asymptote, In Rainbows

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MATH 121 Full Course Notes
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MATH 121 Full Course Notes
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The data below shows the concentration of a chemical produced in a reaction vessel, over time. They grow exponentially, while our graph has an asymptote. The graph has no oscillations or periods. Log graphs do not have a horizontal asymptote. Has a horizontal asymptote, seems like the graph to use. Give a general mathematical form for the function, based on the shape of the graph. Step 1: start with a regular exponential graph. Step 2: we want the graph to decrease in growth on the right. We"ll add a negative to the x value, to flip the graph horizontally. Step 3: we want the graph flipped vertically to further resemble the graph from the question. Step 4: the y-intercept must be at (0, 5), so something needs to be added to the equation to move the graph up. C(t) = (cid:1827)(cid:4666) (cid:4667)+(cid:1828) would be the base to build our equation on.

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