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# Power regression

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This question concers the following data lists

x 3 4 5 6 7 9 10
y 4.6 4.0 3.6 3.3 3.0 2.7 2.5

It is thought that x and y are related by a power relationship, that is, a function of the form y=ax^b.

Perform power regression on these data, and then choose the one option describing a situation which these data could represent.

You should assume in each case that appropriate units have been chosen for x and y, and that the values are quoted to an appropriate accuracy;you should consider only whether or not the power function you have found is appropriate to the situation.

Options

A. X is the time since a pebble was dropped down a well, and y is the distance it has fallen.

B. x is the distance a pebble has fallen, and y is the time since it was dropped.

C. x is the height and y is the radius of a 200ml cylindrical can.

D. x is the radius and y is the height of a 200lm cylindrical can.

E. x is the time and y is the distance from home for someone travelling towards their home at constant speed.

F. x is the time taken to walk between two villages, and y is the average speed of the walker.

G. x is the age of a wooden carving, and y is the amount of radioactive carbon in the carving.

H. x is the amount of radioactive carbon in a carving, and y is its age.