Concept explainers
To find: the logarithmic equation that relates diameter y of a bright common wire nail to its length x .
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Answer to Problem 88E
Explanation of Solution
Given:
The table:
x | 2 | 3 | 4 | 5 | 6 |
y | 0.113 | 0.148 | 0.192 | 0.225 | 0.262 |
Concept Used:
Slope of a line:
The slope of line passing through two point
Slope intercept form of equation of line is
Construct a new table by taking the natural logarithms of the x and y values in the given table.
0.693 | 1.099 | 1.386 | 1.609 | 1.792 | |
-2.180 | -1.910 | -1.650 | -1.492 | -1.339 |
Now plot each point
Now, choose any two points to determine the slope of the line.
So, using the points
Now, from the slope-intercept form of line, the equation of line is:
Where
That is, equation of line is,
Now, to find b , substitute any point
Thus, the equation of line is:
Conclusion:
The logarithmic equation that relates y to x is
Chapter 3 Solutions
EBK PRECALCULUS W/LIMITS
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