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The function [tex]\( h(t) = 210 - 15t \)[/tex] models the altitude of a hot air balloon over time [tex]\( t \)[/tex] in minutes.

Explain what [tex]\( h(10) \)[/tex] means in this real-world scenario and how to find its value.

Sagot :

GinnyAnsweridn
Great question! Let's break it down step-by-step:

### Context
The function [tex]\( h(t) = 210 - 15t \)[/tex] models the altitude of a hot air balloon over time [tex]\( t \)[/tex], where [tex]\( t \)[/tex] is measured in minutes and the altitude [tex]\( h(t) \)[/tex] is measured in feet.

### Question
We are asked to determine the value of [tex]\( h(10) \)[/tex]. This means we want to find the altitude of the hot air balloon after 10 minutes.

### Step-by-Step Solution
1. Substitute [tex]\( t = 10 \)[/tex] into the function [tex]\( h(t) \)[/tex]:
To find [tex]\( h(10) \)[/tex], we substitute [tex]\( t \)[/tex] with 10 in the given function.

[tex]\[ h(10) = 210 - 15 \cdot 10 \][/tex]

2. Perform the multiplication:
Multiply 15 by 10.

[tex]\[ 15 \cdot 10 = 150 \][/tex]

3. Subtraction:
Subtract 150 from 210 to find the altitude.

[tex]\[ 210 - 150 = 60 \][/tex]

### Answer
The value of [tex]\( h(10) \)[/tex] is 60.

### Interpretation
In the context of the real-world scenario, [tex]\( h(10) = 60 \)[/tex] means that after 10 minutes, the altitude of the hot air balloon is 60 feet.

So, after carefully substituting and calculating, we find that the altitude of the hot air balloon after 10 minutes is 60 feet.
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