Sure, I'd be happy to explain.
In this scenario, the function [tex]\( h(t) = 210 - 15t \)[/tex] models the altitude of a hot air balloon, where:
- [tex]\( h(t) \)[/tex] is the altitude of the hot air balloon in meters after [tex]\( t \)[/tex] minutes,
- [tex]\( 210 \)[/tex] meters is the initial altitude of the hot air balloon,
- [tex]\( 15 \)[/tex] meters per minute represents the rate at which the hot air balloon descends.
To understand what [tex]\( h(10) \)[/tex] means, let's break it down step by step:
1. Identify the function: [tex]\( h(t) = 210 - 15t \)[/tex].
2. Substitute [tex]\( t = 10 \)[/tex] into the function: We need to find [tex]\( h(10) \)[/tex], which is the altitude of the hot air balloon after 10 minutes.
3. Perform the calculation:
[tex]\[
h(10) = 210 - 15 \times 10
\][/tex]
4. Simplify the expression:
[tex]\[
15 \times 10 = 150
\][/tex]
Therefore,
[tex]\[
h(10) = 210 - 150
\][/tex]
5. Calculate the result:
[tex]\[
h(10) = 60
\][/tex]
In the context of this real-world scenario, [tex]\( h(10) = 60 \)[/tex] means that after 10 minutes, the altitude of the hot air balloon is 60 meters above the ground.
