To Calculate: The air density at
(A)
(B)
(C)
(D)
Given: The air density model is given as
Where;
Concept used:
(1) If a function
(2) An exponential model or function is as follows:
Calculation:
(A)Firstly take the air density model
Thus,
(B)Now simplify the air model
Then, rewrite the above air pressure model.
Take on both sides a logarithm with a natural base
Therefore,
And also given the air pressure
Thus,
(C) Similarly, again take the air density model
Then, rewrite the above air density model.
Take on both sides a logarithm with a natural base
Therefore,
Thus,
....... (2)
So equation (1) and equation (2), equate
Therefore,
Hence,
Air pressure is directly proportional to air density. If the air density is increased then the air pressure will also increase, and vice versa.
(D) To check and explain the general rule which says that for every
The air pressure model is given as follows:
Solve for
Also, know that;
So,
The difference between
We obtained a
Conclusion: Hence, the air density
And air pressure model is true for the height
If the air density is increased then the air pressure will also increase or air pressure is directly proportional to air density.
Disagree with the general rule which states that there is only a
Chapter 4 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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