(a)
To find: The
(a)
Answer to Problem 9AYU
The scatter plot is shown in Figure 4
Explanation of Solution
Given:
The given table for the number of subscribers is shown in Table 1
Table 1
Years | Subscribers |
1975(t=5) | 9,800 |
1980(t=10) | 17,500 |
1985(t=15) | 35,440 |
1990 (t= 20) | 50,520 |
1992 (t= 22) | 54,300 |
1994 (t= 24) | 58,373 |
1996 (t= 26) | 62,300 |
1998 (t= 28) | 64,650 |
2000 (t=30) | 66,250 |
2002 (t=32) | 66,472 |
2004 (t=34) | 65,727 |
2006(t=36) | 65,319 |
Calculation:
From the given data TI-83 Calculator to plot the scatter diagram.
Consider
First turn On the stat plot 1, the diagram for the snip is shown in Figure 1
Figure 1
Then go to STAT+1 to enter the list.
Figure 2
Adjust the window so the calculator can show the scatter plot in the screen as shown in Figure 3
Figure 3
Graph the scatter plot as shown in Figure 4
Figure 4
(b)
To find: The logistic model of the given data.
(b)
Answer to Problem 9AYU
The logistic model is
Explanation of Solution
In the graphing calculator press the STAT then click the CALC menu, the snip for the calculator is shown in Figure 5
Figure 5
To use, the logistic function to fit the data we pick the option B logistic then Enter button as shown in Figure 6
Figure 6
From above, the value model is,
(c)
To find: The scatter plot for the logistic model.
(c)
Answer to Problem 9AYU
The scatter plot is shown in Figure 7
Explanation of Solution
Consider the expression for the logistic model is,
Enter Y= button, the snip is shown in Figure 7
Figure 7
The scatter plot is shown in Figure 7
Figure 7
(d)
To find: The maximum number of cable TV subscribers in the United States.
(d)
Answer to Problem 9AYU
The maximum number of TV subscriber is
Explanation of Solution
Consider the expression for the logistic model is,
For
Then,
Thus, the maximum number of TV subscriber is
(e)
To find: The model found in part (b) to predict the number of cable TV subscriber in the United States in 2015.
(e)
Answer to Problem 9AYU
The maximum number of TV subscriber is
Explanation of Solution
Consider the expression for the logistic model is,
To find the maximum number of subscriber in 2015 substitute 45 for
Then,
Thus, the maximum number of TV subscriber is
Chapter 5 Solutions
Precalculus
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