Question 86858: The height of a hot-air balloon was measured at different times as the balloon descended. A record of the heights and times is shown in the table below.
time(t) in minutes 1 2 3 4
Height (h) in meters 76 64 44 16
Based on the table, which of the following equations expresses the relationship between h and t?
(1) h = 60 + 16t
(2) h = 70 + 6t
(3) h = 80 - 4t
(4) h = 80 - 4t squared
(5) h = 90 - 14t squared
I don't understand this problem at all? Could you please solve?
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! You have coordinates: (t,h)
time(t) in minutes 1 2 3 4
Height (h) in meters 76 64 44 16
So:
(1,76), (2,64), (3,44), (4,16)
Obviously, the equation would not be linear due to the fact that after each minute the height doesn't change by a constant number.
(4) h = 80 - 4t squared
(5) h = 90 - 14t squared
Are the only two choices....
Now, we should plug in a value:
(4) h = 80 - 4(1) squared = 80 - 4 = 76
(5) h = 90 - 14(1) squared = 90 - 14 = 76
So, for each we have: (1,76) ... which applies to the value above
Now, we should plug in a different value:
(4) h = 80 - 4(2) squared = 80 - 16 = 64
(5) h = 90 - 14(2) squared = 90 - 56 = 34
(4) is the only equation that suits our two values ...
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