David is conducting an experiment to estimate the acceleration of an object due to gravity. He takes a ball, drops it from different heights, and records the time that it takes for the ball to hit the ground using an optic laser connected to a stop watch. He collects the following data:

The theory of physics states that the distance that an object falls depends on time through a power equation.

(a) Draw a scatter diagram treating time as the explanatory variable.

(b) Determine the logarithm of both the x- and y-values so that X = log x and Y = log y. Draw a scatter diagram of the transformed data.

(c) Find the least-squares regression line of the transformed data.

(d) Find the power equation of best fit.

(e) Use the power equation of best fit to predict the distance the object will fall in 1.85 seconds.

(f) Physics theory states that the distance that an object falls is given by the equation s = 1/2gt², where s is distance, g is acceleration due to gravity, and t is time. What is David’s estimate of g? (It is known that the acceleration due to gravity is approximately 32 feet/second².)