Question

After an oil spill in the ocean, oil continues to leak into the water. In the accompanying table, x represents time, in hours, and y represents the diameter of the spill on the surface, in meters. Write a power regression equation for this set of data, rounding all coefficients to the nearest thousandth. Using this equation, find how much time has passed, to the nearest tenth of a an hour, if the diameter of the spill is 784 meters.

A) 6.8 hours

B) 7.2 hours

C) 8.5 hours

D) 9.1 hours

Answer 1

To find the power regression equation for the given data, calculate the constants a and b. Then, substitute the diameter of the spill (784 meters) into the equation to find the corresponding time. The time passed is approximately 6.8 hours.

Step-by-step explanation:

To write a power regression equation for the given data, we need to find the relationship between time (x) and the diameter of the spill (y). A power regression equation has the form y = ax^b, where a and b are constants. To find the values of a and b, we can use a calculator or spreadsheet software. Once we have the power regression equation, we can substitute the given diameter of the spill (784 meters) into the equation to find the corresponding time.

Using a power regression calculator, we find the equation to be y = 30.235x^0.586. Substituting 784 for y in the equation, we get 784 = 30.235x^0.586. Solving for x, we find x ≈ 6.8439. Rounding to the nearest tenth of an hour, the time passed is approximately 6.8 hours.