The following table shows natural gas production N in trillions of cubic feet in the United States t years after 1940.t = years since 1940N = cubic ft. in trillions3.75108.482015.093023.794021.875021.526024.15(a) Make a logistic model for N as a function of t.12.54o N(t)-0.35t1 + 5.94e35.67o N(t)1 + 3.41e-1.25t23.31o N(t)-0.14t1 + 6.99e29.53o N(t)-0.88t1 + 7.58e34.86o N(t) =1 + 8.54e-0.91t(b) Graph the data and the logistic model.N30302525202015151010551020304050607010203040506070N303025252020151510F1051020304050607010203040506070(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

Answer:- 1)Option a is the right answer. 2)Option a.

t- years since 1940 N- cubic ft. in trillions 3.75 10 8.48 15.09 20 30 23.79 40 21.87 50 21.52 60 24.15 (a) Make a logistic model for N as a function of t. 12.54 O N(t) = 1+ 5.94e-0.35t 35.67 O N(t) = 1+ 3.41e-1.25 23.31 O N(t) = 1 + 6.99e -0.14t 29.53 o N(t) = 1+ 7,58e-0.88t 34.86 O N(t) = 1 + 8.54e-0.91t (b) Graph the data and the logistic model. N 30 30 25 25 20 20 15 15 10 10 10 20 30 40 50 60 70 10 20 30 40 50 60 70 30 30 25 25 20 20 15 15 10 10 10 20 30 40 50 60 70 10 20 30 40 50 60 70 (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

t- years since 1940 N- cubic ft. in trillions 3.75 10 8.48 15.09 20 30 23.79 40 21.87 50 21.52 60 24.15 (a) Make a logistic model for N as a function of t. 12.54 O N(t) = 1+ 5.94e-0.35t 35.67 O N(t) = 1+ 3.41e-1.25 23.31 O N(t) = 1 + 6.99e -0.14t 29.53 o N(t) = 1+ 7,58e-0.88t 34.86 O N(t) = 1 + 8.54e-0.91t (b) Graph the data and the logistic model. N 30 30 25 25 20 20 15 15 10 10 10 20 30 40 50 60 70 10 20 30 40 50 60 70 30 30 25 25 20 20 15 15 10 10 10 20 30 40 50 60 70 10 20 30 40 50 60 70 (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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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
8.48
20
15.09
30
23.79
40
21.87
50
21.52
60
24.15
(a) Make a logistic model for N as a function of t.
12.54
o N(t)
-0.35t
1 + 5.94e
35.67
o N(t)
1 + 3.41e-1.25t
23.31
o N(t)
-0.14t
1 + 6.99e
29.53
o N(t)
-0.88t
1 + 7.58e
34.86
o N(t) =
1 + 8.54e-0.91t
(b) Graph the data and the logistic model.
N
30
30
25
25
20
20
15
15
10
10
5
5
10
20
30
40
50
60
70
10
20
30
40
50
60
70
N
30
30
25
25
20
20
15
15
10F
10
5
10
20
30
40
50
60
70
10
20
30
40
50
60
70
(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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