Certainly! Let's break this problem down step by step.
### Understanding the Function
The function given is [tex]\( h(t) = 210 - 15t \)[/tex], where:
- [tex]\( h(t) \)[/tex] represents the altitude of the hot air balloon at time [tex]\( t \)[/tex] (in minutes).
- [tex]\( t \)[/tex] is the time in minutes.
- The term [tex]\( 210 \)[/tex] represents the initial altitude of the balloon.
- The term [tex]\( -15t \)[/tex] represents the rate at which the altitude decreases over time.
### Finding [tex]\( h(10) \)[/tex]
Step 1: Interpret the Question
We are asked to find [tex]\( h(10) \)[/tex], which means we need to determine the altitude of the hot air balloon at [tex]\( t = 10 \)[/tex] minutes.
Step 2: Substitute [tex]\( t = 10 \)[/tex] into the Function
Plug [tex]\( t = 10 \)[/tex] into the given function:
[tex]\[ h(10) = 210 - 15 \cdot 10 \][/tex]
Step 3: Perform the Calculation
Let's calculate the value step by step:
1. Multiply [tex]\( 15 \)[/tex] by [tex]\( 10 \)[/tex]:
[tex]\[ 15 \cdot 10 = 150 \][/tex]
2. Subtract this product from [tex]\( 210 \)[/tex]:
[tex]\[ 210 - 150 = 60 \][/tex]
### Conclusion
Therefore, [tex]\( h(10) \)[/tex] equals [tex]\( 60 \)[/tex]. This means that the altitude of the hot air balloon, 10 minutes after it started descending, is [tex]\( 60 \)[/tex] units (the units of altitude are not specified but they might be meters, feet, etc., according to the context of the problem).
