5.3 Modeling with Power Functions. Power Data & Linear Data Connection. If f is a power function of x, then ln(f) is a linear function of ln(x). Getting a Power Model from Data. Ex. 1) Volume Inside a Sphere.
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Getting a Power Model from Data
a.)Plot the graph of ln(V) versus ln(r) to determine whether or not it is reasonable to think that the volume is related to the radius by a power function.
b.) Use regression to find a formula for the line formed by the plot of ln(V) as a function of ln(r). Then, use that formula to write a formula for the volume of a sphere. Round parameters to 2 decimal places.
c.) Use regression to find a formula for the volume of a sphere as a function of the radius. Round to 2 decimal places.
d.) Plot both the function from b and c and the original data point on the same graph.
e.) What is the radius of a sphere with a volume of 453.25? (Use the function from part c.
a.) Make a power model for weight versus height.
b.) According to the model from part a, what percentage increase in weight can be expected if height is increased by 10%?