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25 May, 22:07

A hot air balloon descends to the ground. The function a (t) = 210 - 15t can be used to describe the altitude of the balloon as it approaches the ground. The time is in minutes.

What does t represent?

altitude of the balloontime after the balloon begins to descendtime it takes the balloon to reach the ground

What does a (t) represent?

altitude of the balloontime after the balloon begins to descendtime it takes the balloon to reach the ground

What information will a (5.5) give?

time it takes the balloon to reach an altitude of 5.5 feetaltitude of the balloon after 5.5 minutestime it will take the balloon to reach the ground, or 5.5 minutes

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Answers (1)
  1. 26 May, 00:03
    0
    As time goes on, the balloon gets closer and closer to the ground, or it's at a lower altitude. This means that the altitude depends on how much time has passed. Since you can use the variable t to predict the altitude, just as you would use the amount of time that has passed, t actually is the amount of time that has passed. Therefore t represents time.

    I said before that you can predict the height using time. In this equations, there are only two unknowns: the amount of time that has passed, and the height. Since we already know time is represented by "t", we can figure that a (t) represents the height after any specific time. Think of a (t) as the y value, and t as the x value. We need to find x first in order to find y, just like we need a specific t-value (time) to find the height at that time. This is why the y value, a (t), is written like it is, because the altitude (a) is found by plugging in a time (t). So a (t) is the altitude of the balloon.

    We already know that a (t) is the altitude at any time. a (5.5) is the altitude at a very specific time, or the altitude of the balloon at 5.5 minutes.
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