The data below describe the height of a cell phone accidentally dropped off a rooftop ledge as it falls to the ground.
Time Since Dropped
(seconds) Height Above Ground
(meters)
0.0 25.0
0.5 24.0
1.0 20.0
1.5 14.0
2.0 5.5
Quadratic regression is used to model this data. According to regression, how long did it take for the cell phone to fall to a height of 17 meters above the ground?
a
1.1 seconds
b
1.3 seconds
c
1.5 seconds
d
1.7 seconds
Based on the quadratic regression model, the time it took for the cell phone to fall to a height of 17 meters above the ground can be estimated. By plugging in the value of 17 meters for the height and solving for the time, we can find the answer.
Using the quadratic regression equation, we have:
Height = -6.7143t^2 + 24.571t + 25
Plugging in 17 for the height:
17 = -6.7143t^2 + 24.571t + 25
Rearranging the equation to solve for t:
-6.7143t^2 + 24.571t + 8 = 0
Solving this quadratic equation, we find two potential values for t: t≈1.47 and t≈1.68
Therefore, according to the regression, it took approximately 1.5 seconds (option c) for the cell phone to fall to a height of 17 meters above the ground.