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Linear and Exponential Model Transformation Exercises, Exams of Mathematical Modeling and Simulation

A series of exercises focused on transforming linear and exponential models. It includes data points, calculations, and steps for transforming data and deriving equations for both linear and exponential models. Practical examples and calculations to illustrate the process of model transformation.

Typology: Exams

2024/2025

Uploaded on 03/23/2025

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maria-fernanda-urbano-lopez 🇺🇸

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Temperatura Viscosidad
n Xi Yi Ln yi X^2
1 85.63 0.27 -1.30933332 7332.4969
2 64.48 0.4 -0.9162907319 4157.6704
3 42.12 0.62 -0.4780358009 1774.0944
4 76.73 0.31 -1.1711829815 5887.4929
5 58.18 0.46 -0.7765287895 3384.9124
6 42.35 0.6 -0.5108256238 1793.5225
n= 6 369.49 2.66 -5.1621972476 24330.1895
136522.8601
Modelo lineal transformado
𝑚=((6)(−348.0122)−(369.49)
(−5.1621))/((6)
(24330.189)−(136522.860))=
𝒚_𝒊=𝒃_𝟎+𝒎𝒙
𝑚=(𝑛𝛴(𝑥𝑦)−𝛴×𝛴𝑦)/(𝑛∑128▒𝑥^2 −(∑128▒𝑥)^2 )
𝑏_0=(∑128 〖𝑦𝛴𝑥 ^2 −∑128▒𝑥 ∑128▒(𝑥𝑦) )/(𝑛∑128▒𝑥^2 −(𝛴𝑥)^2 )
(∑▒𝑥)^2=
𝑏_0=((−5.162)(24330.189)−(369.49)(−348.0122))/((6)(24330.189)−136522.860)=
𝒍𝒏 〖𝒚 _𝒊 =𝒍𝒏 〖𝒃 _𝟎 +𝒃_𝟏 𝒙_𝟏
𝑦_𝑖=0.316−0.019(85.63)=−1.310
𝒚_𝒊=𝒃_𝟎 ^(𝒃_𝟏 𝒙)
ln 〖𝑏 _0 =0.316
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𝒚=𝟏.𝟑𝟕𝟏𝟖∗(ⅇ^(^−𝟎.𝟎𝟏𝟗𝒙) )
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Temperatura Viscosidad n Xi Yi Ln yi X^ 1 85.63 0.27 -1.30933332 7332. 2 64.48 0.4 -0.9162907319 4157. 3 42.12 0.62 -0.4780358009 1774. 4 76.73 0.31 -1.1711829815 5887. 5 58.18 0.46 -0.7765287895 3384. 6 42.35 0.6 -0.5108256238 1793. n= 6 369.49 2.66 -5.1621972476 24330. 136522. Modelo lineal transformado

𝒚𝒊=𝒃𝟎+𝒎𝒙

𝑚=(𝑛𝛴(𝑥𝑦)−𝛴×𝛴𝑦)/(𝑛∑128▒𝑥^2 −(∑128▒𝑥)^ 2 )

=(∑128▒ 〖𝑦𝛴𝑥 ^ 2 〗−∑ 128▒𝑥 ∑128▒(𝑥𝑦) )/(𝑛∑128▒𝑥^2 −(𝛴𝑥)^ 2 )

(∑▒𝑥)^2=

𝑏_0=((−5.16 2 )(24330.1 89 )−(369.49)(−34 8. 0122 ))/((6)(24330. 189 )−136522.

𝒍𝒏 〖𝒚  𝒊 〗 =𝒍𝒏 〖𝒃 𝟎 〗 +𝒃𝟏 𝒙 '𝟏

𝑦 '_𝑖=0.316−0.019(85.63)=−1.

𝒚 '𝒊=𝒃𝟎 ⅇ^(𝒃_𝟏 𝒙)

ln 〖𝑏 _ 0 〗 =0.

𝒚 '=𝟏.𝟑𝟕𝟏𝟖∗(ⅇ^(^−𝟎.𝟎𝟏𝟗𝒙) )

ln 〖𝑏 _ 0 〗 =0. 𝑏0=ⅇ^0.316= 𝑦 '𝑖=1.37ⅇ^(−0.01 9 𝑥 '_𝑖 ) 0

XY

𝑚=(𝑛𝛴(𝑥𝑦)−∑128▒ 〖𝑥∑ 128▒𝑦 〗 )/(𝑛𝛴𝑥^2−(∑128▒𝑥)^2 )

𝑏=(∑128▒ 〖𝑦𝛴𝑥 ^2 〗− 𝛴𝑥𝛴 ×𝑦)/(𝑛∑128▒𝑥^2 −(𝑥)^2 )

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