Concept explainers
Hurricanes Hurricanes are categorized using the Saffir-Simpson Hurricane Scale, with winds 111-130 miles per hour (mph) corresponding to a category 3 hurricane, winds 131-155 mph corresponding to a category 4 hurricane, and winds in excess of 155 mph corresponding to a category 5 hurricane. The following data represent the number of major hurricanes in the Atlantic Basin (category 3, 4, or 5) each decade from 1921 to 2010.
(a) Draw a
(b) Find a sinusoidal function of the form that models the data.
(c) Draw the sinusoidal function found in part on the scatter diagram.
(d) Use a graphing utility to find the sinusoidal function of best fit.
(e) Graph the sinusoidal function of best fit on a scatter diagram of the data.
To find:
a. Draw a scatter diagram of the data.
Answer to Problem 29AYU
a.
Explanation of Solution
Given:
Calculation:
a. Draw a scatter diagram of the data.
To find:
b. Find a sinusoidal function of the form that models the data.
Answer to Problem 29AYU
b.
Explanation of Solution
Given:
Calculation:
b. Find a sinusoidal function of the form that models the data.
Determine , the amplitude of the function.
Determine , the vertical shift of the function.
Determine , It is easier to find the horizontal stretch factor first. Since the temperatures repeat every 5 hurricanes, the period of the function is . Because . Therefore .
Now superimpose the graph of on the scatter diagram. See Figure, where it is clear that the graph still needs to be shifted horizontally.
Determine the horizontal shift of the function by using the period of the data. we must shift the graph of the function .
To find:
c. Draw the sinusoidal function found in part (b) on the scatter diagram.
Answer to Problem 29AYU
c.
Explanation of Solution
Given:
Calculation:
c. Draw the sinusoidal function found in part (b) on the scatter diagram.
To find:
d. Use a graphing utility to find the sinusoidal function of best fit.
Answer to Problem 29AYU
d.
Explanation of Solution
Given:
Calculation:
d. Use a graphing utility to find the sinusoidal function of best fit.
To find:
e. Graph the sinusoidal function of best fit on a scatter diagram of the data.
Answer to Problem 29AYU
e.
Explanation of Solution
Given:
Calculation:
e. Graph the sinusoidal function of best fit on a scatter diagram of the data.
Chapter 6 Solutions
Precalculus Enhanced with Graphing Utilities
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