(a)
To find: The
(a)
Explanation of Solution
Given:
The given table is shown in table 1
Table 1
Month, | Average Monthly Temperature, |
January 1 | 31.8 |
February 2 | 34.8 |
March 3 | 44.1 |
April 4 | 53.4 |
May 5 | 63.4 |
June 6 | 72.5 |
July 7 | 77.0 |
August 8 | 75.6 |
September 9 | 68.5 |
October 10 | 56.6 |
November 11 | 46.8 |
December 12 | 36.7 |
Calculation:
The scatter plot of the given data is shown in Figure 1
Figure 1
(b)
To find: The sinusoidal function of the given form.
(b)
Answer to Problem 32AYU
The required sinusoidal function is
Explanation of Solution
Given:
The given form of the sinusoidal function is,
Calculation:
Consider the given sine function is,
Consider the amplitude
Then,
Consider the expression for the vertical shift of the sinusoidal function is,
Then,
Consider the expression for the time period of the data is,
As the data repeats after every 12 months, then,
Consider the horizontal shift is determined by dividing the 12 in four equal parts as,
Since, the curve increases in the interval of
Then, the expression for the sinusoidal function is,
(c)
To find: The scatter plot for the function found in part (b).
(c)
Answer to Problem 32AYU
The required plot is shown in Figure 2
Explanation of Solution
Consider the sinusoidal function is,
The graph for the sinusoidal model is shown in Figure 2
Figure 2
(d)
To find: The sinusoidal function of the best fit model.
(d)
Answer to Problem 32AYU
The best fit model is
Explanation of Solution
The best fit model with the help of graphing calculator is,
(e)
To find: The sinusoidal function of best fit on the scatter diagram of the data.
(e)
Answer to Problem 32AYU
The plot for the best fit model is shown in Figure 3
Explanation of Solution
Consider the best fit model is,
The sinusoidal plot for the best fit model is shown in Figure 3
Figure 3
Chapter 6 Solutions
Precalculus
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