Concept explainers
a.
To determine the regression feature of a graphing utility to attempt to find the logarithmic model and explain why the result is an error message.
a.
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Answer to Problem 32E
The logarithmic model
Explanation of Solution
Given:
Consider the given information,
and the data provided are (0,1),(10,0.25),(20,0.06),(5,0.55),(15,0.12),(25,0.02)
For the given data, it is understood that the point (0,1) has an error because from the given expression if (h, p) = (0,1) then it is clear that 0 is not in the domain of ln.
b.
To determine the regression feature of the graphing utility to find the logarithmic model for the data.
b.
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Answer to Problem 32E
The logarithmic model for the data is
Explanation of Solution
Given:
Consider the given expression,
Graph:
Calculation:
From the given expression,
Reversing the expression, it can be written as
As,
Conclusion:
Therefore, the logarithmic model is
c.
To graph: using graphing utility to plot the data and the logarithmic model in the same viewing window.
c.
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Explanation of Solution
Given information: Consider the data given,
(0,1),(10,0.25),(20,0.06),(5,0.55),(15,0.12),(25,0.02)
Graph:
Interpretation: as from the following graph, it is clear that the data is fitted with the logarithmic model.
d.
To estimate the altitude using the model at a given pressure.
d.
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Answer to Problem 32E
The altitude at a given pressure using the model is
Explanation of Solution
Given:
Consider the given information,
Pressure of the model is 0.75 atmosphere.
Calculation:
From the given data,
Pressure = 0.75atm
Altitude = 0.863-6.447
Conclusion:
Therefore, the altitude of the model is
e.
To estimate the pressure at an altitude of given kilometer.
e.
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Answer to Problem 32E
The pressure at the altitude given is 0.15 atmosphere.
Explanation of Solution
Given:
The altitude for the model given is 13km.
Calculation:
From the graph, at altitude = 13km the pressure is 0.15 atmosphere.
Chapter 3 Solutions
EP PRECALC.GRAPHING APPR.-WEBASSIGN-1YR
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