c) Which year's production was farthest from the prediction of the logistic model? (d) What does the logistic model predict for the amount of natural gas that will be produced in the long run? Note: In other contexts, this would be known as the carrying capacity. (Use the model found in part (a).)  ____ trillion

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(c) Which year's production was farthest from the prediction of the logistic model?


(d) What does the logistic model predict for the amount of natural gas that will be produced in the long run? Note: In other contexts, this would be known as the carrying capacity. (Use the model found in part (a).)
 ____ trillion

 

The following table shows natural gas production N in trillions of cubic feet in the United States t years after 1940.
t= years since 1940
N = cubic ft. in trillions
3.75
10
20
30
40
50
60
8.48
15.09
23.79
21.87
21.52
24.15
(a) Make a logistic model for N as a function of t.
23.31
N(t) =
1+ 6.99e-0.14
12.54
O N(e) :
1+ 5.94e 0.35t
%3D
35.67
O N(e) =
1+ 3.41e125
29.53
O N(e)
1+ 7.58e0.BBt
%3!
34.86
O N(t)
1+ 8.54e-0.91t
%3D
(b) Graph the data and the logistic model.
N
N
30
30
25
25
20
20
15
15
10
10
5
10
20
30
40 50
60
70
10
20
30 40
50
60
70
3아
30
25
25
20
20
15
15
10
10
5
wwwt
10
20
30
40
50
60
70
10
20
30 40
50
60
70
Transcribed Image Text:The following table shows natural gas production N in trillions of cubic feet in the United States t years after 1940. t= years since 1940 N = cubic ft. in trillions 3.75 10 20 30 40 50 60 8.48 15.09 23.79 21.87 21.52 24.15 (a) Make a logistic model for N as a function of t. 23.31 N(t) = 1+ 6.99e-0.14 12.54 O N(e) : 1+ 5.94e 0.35t %3D 35.67 O N(e) = 1+ 3.41e125 29.53 O N(e) 1+ 7.58e0.BBt %3! 34.86 O N(t) 1+ 8.54e-0.91t %3D (b) Graph the data and the logistic model. N N 30 30 25 25 20 20 15 15 10 10 5 10 20 30 40 50 60 70 10 20 30 40 50 60 70 3아 30 25 25 20 20 15 15 10 10 5 wwwt 10 20 30 40 50 60 70 10 20 30 40 50 60 70
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