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Power Models & Proportionality
Modeling with functions of the form axn, and the concept of direct and inverse variation
Modeling with functions of the form axn, and the concept of direct and inverse variation
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Directly proportional quantities are constant multiples of each other. In the context of modelling, we typically say, "y varies directly with xn," which means y=kxn for some constant k. This can be denoted y∝xn.
If y is directly proportional to xn, then x=0⟺y=0.
If y is directly proportional to xn, then if x increases (or decreases) by a factor of c, y increases (or decreases) by a factor of cn.
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If y varies inversely with xn, then y=xnk.
If y is inversely proportional to xn (y∝xn1), then the y-axis is an asymptote of the graph of y=f(x).
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