To find: the logarithmic equation that relates an animal’s weight x (in pounds) and its lowest stride frequency while galloping y (in strides per minute).
Answer to Problem 87E
Explanation of Solution
Given:
The table:
x | 25 | 35 | 50 | 75 | 500 | 1000 |
y | 191.5 | 182.5 | 173.8 | 164.2 | 125.9 | 114.2 |
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.
3.219 | 3.555 | 3.912 | 4.317 | 6.215 | 6.908 | |
5.255 | 5.208 | 5.158 | 5.101 | 4.835 | 4.738 |
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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