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

 
 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
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1 Answer

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.
 

Comments

Thanks so much!!! The problem also Had a question about velocity is that important in regards to the other questions? And I do need to know how to put the data in the calculator I think I have an idea but I'm not sure!! 
Thanks again
I am using a TI-84 Plus Graphing Calculator. First you need to enter times and heights. STAT-EDIT-enter the times under list 1 (L1) and the heights under list 2 (L2). Hit 2nd Quit.  Then, STAT-CALC-LINREG(ax + b)-ENTER.  That gives you the equation for a straight line.
 
Enter STAT-CALC-QUADREG-ENTER. Then, you have the equation for a quadratic function (parabola). Follow the same steps for other regressions.
 
To graph your equations, hit Y=, VARS, Statistics, Arrow over to EQ, Enter. Then hit graph.
 
Hope that helps.