Ahot air ballon was 249 ft above the ground. it decreased its altitude by 61/2 ft per min for 15 min, and then increased its altitude by 9 ft. what was the ballon’s overall change in altitude. write an expression to model the situation. what is the hot air ballons elevation. plz i will give you 100 points

a) Change in altitude

The altitude decreased 6.5 ft/min for 15 min, so the change in that time was ...

... (-6.5 ft/min)×(15 min) = -97.5 ft

Then the altitude increased 9 ft, so the overall change was ...

... -97.5 ft + 9 ft = -88.5 ft

b) Expression to model the situation

As with many "this situation" problems, it is not clear exactly what we're to model. In simplest terms the model can be ...

... final altitude = initial altitude + change in altitude

... final altitude = 249 ft - 88.5 ft . . . . . . . . an equation to model the situation

Then the final altltude is ...

... final altitude = 160.5 ft . . . . . . carry out the subtraction

Comment on the model of "this situation"

If you try to write a model that shows altitude as a function of time, you run into a problem after 15 minutes. The altitude increases by 9 ft in an unspecified period of time that we know cannot be zero.

You cannot rightly model the altitude as a function of time by adding that 9 ft to the initial altitude, as it only comes into play after 15 minutes.

Thus, it seems the only reasonable model is one that gives the final altitude after 15 minutes (plus some additional unspecified period). That is the model we have presented above.