A super hero leaps from a building to capture a villain the data from his leap is shown below

Question

 

 Time(seconds)  .75  | 1.5 |  2   | 2.25  |   2.75  |   3.5     

  Height(feet)    108  | 119 | 116|  112  |   97     |     59    

 

 

 1. What type of function best models this data

 linear exponential quadratic or other 

 

 2. Use a graphing calculator to perform a regression for the best fit equation. Write the resulting equation below, rounding to the nearest hundredth.

 

 3. Calculate how many seconds it takes for the super hero to land on the ground (assume no flying powers used) show your work and round to the nearest hundredth

Answer 1

linear regression: y = -17.77x + 139.59

Using this equation, let y = 0 which would be the number of feet at ground level: 0 = -17.77x + 139.59.        Thus solving for x, he would hit the ground in 7.86 sec.

 

Quadratic regression: y = -16.29x² + 51.45x + 78.52

This equation isn't feasible because his jump would take the shape of a parabola. If he was being shot out of a cannon, this equation would make more sense.

 

Exponential regression:  y = 154.98(.81)^x

This equation isn't logical either since with a decreasing exponential equation, technically he would never hit the ground.

 

Do you know how to enter the data into a graphing calculator?  If not, let me know.