(a)
To find: The
(a)
Answer to Problem 29AYU
The scatter plot is shown in Figure 1
Explanation of Solution
Given:
The given data is shown in Table 1
Table 1
Month | Average Monthly Temperature F |
1 | 24.2 |
2 | 28.4 |
3 | 32.7 |
4 | 39.7 |
5 | 47.0 |
6 | 53.0 |
7 | 56.0 |
8 | 55.0 |
9 | 49.4 |
10 | 42.2 |
11 | 32.0 |
12 | 27.1 |
Calculation:
The data of the table represents the average monthly temperature over a period of one year. The scatter diagram is drawn by taking months along the x axis and the average monthly temperature along the y axis.
Figure 1
(b)
To find: The sinusoidal function of the form
(b)
Answer to Problem 29AYU
The sinusoidal model is
Explanation of Solution
Consider the form of the sinusoidal function is,
Consider the amplitude of the sinusoidal function is,
Consider the value of the vertical shift is,
Consider the time period of the sinusoidal function is,
The time is divided into four sub intervals as
The local maximum is at
The local minimum is at
The required horizontal shift is 4 units to the right.
So, the sinusoidal model is,
(c)
To find: The scatter diagram for the sinusoidal function found in part (c).
(c)
Explanation of Solution
Consider the sinusoidal function is,
The sinusoidal function scatter plot with the help of graphing utility is shown in Figure 2
Figure 2
(d)
To find: The best fit sinusoidal function.
(d)
Answer to Problem 29AYU
The expression for the best fit curve is
Explanation of Solution
Consider the sinusoidal function is,
Consider the best fit curve with the help of graphing utility is,
(e)
To find: The plot of sinusoidal function of best fit.
(e)
Answer to Problem 29AYU
The plot is shown in Figure 3
Explanation of Solution
Consider the best fit function is,
The scatter plot for the best fit function is shown in Figure 3
Figure 3
Chapter 6 Solutions
Precalculus
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