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? What does a(t) represent? What information will a(5) give?

Answer 1

In the function \( a(t) = 210 - 15t \):

• \( t \) represents the time in minutes since the hot air balloon started its descent.
• \( a(t) \) represents the altitude of the hot air balloon in feet at time \( t \).

To evaluate \( a(5) \), you substitute \( t = 5 \) into the function:

\[ a(5) = 210 - 15(5) = 210 - 75 = 135 \]

Therefore, \( a(5) \) gives the altitude of the balloon at 5 minutes after the descent has started, which is 135 feet above the ground.