Question

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(5.5) give?

Answer 1

[AI-generated answer — Bot GPT-4o]

Let's break down the given information and the function to fully understand what each part represents.

1. **What does \( t \) represent?**

\( t \) represents the time in minutes since the balloon started descending.

2. **What does \( a(t) \) represent?**

\( a(t) \) represents the altitude of the hot air balloon (in presumably feet or meters) at time \( t \) minutes after the descent starts.

3. **What information will \( a(5.5) \) give?**

\( a(5.5) \) will give the altitude of the hot air balloon 5.5 minutes after it started descending.

To find \( a(5.5) \):

\[
a(5.5) = 210 - 15 \cdot 5.5
\]

\[
a(5.5) = 210 - 82.5
\]

\[
a(5.5) = 127.5
\]

So, \( a(5.5) \) gives the information that the altitude of the balloon is 127.5 units (e.g., feet or meters) 5.5 minutes after it started descending.