Power models of the form y=axb or y∝xb,
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.
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).
Proportionality relations can be used to build models called power models, which have the form
which is equivalent to saying y∝xb.
Power models can be found from given data using your calculator's power regression feature.
Nice work completing Power Models & Proportionality , here's a quick recap of what we covered:
Exercises checked off
Power models of the form y=axb or y∝xb,
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.
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).
Proportionality relations can be used to build models called power models, which have the form
which is equivalent to saying y∝xb.
Power models can be found from given data using your calculator's power regression feature.
Nice work completing Power Models & Proportionality , here's a quick recap of what we covered:
Exercises checked off