Grandfather clocks use pendulums to keep accurate time. The relationship between the length of a pendulum L and the time T for one complete oscillation can be expressed by the equation L = kTⁿ, where k is a constant and n is a positive integer to be determined. The data in the table were taken for different lengths of pendulums.

(a) As the length of the pendulum increases, what happens to T?

(b) Use the data to approximate k and determine the best value for n.

(c) Using the values of k and n from part (b), predict T for a pendulum having length 5 ft. Round to the nearest hundredth.

(d) If the length L of a pendulum doubles, what happens to the period T ?

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L (ft) L (ft) T (sec) T (sec) 1.0 1.11 3.0 1.92 1.36 1.5 3.5 2.08 2.0 1.57 4.0 2.22 1.76 2.5