The energy of a system is given as E ( t ) = α 3 e − βt , where t is the time and β = 0.3 s − 1 . The errors in the measurement of α and t are 1.2% and 1.6% , respectively. At t = 5 s , maximum percen

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The energy of a system is given as E ( t ) = α 3 e − βt , where t is the time and β = 0.3 s − 1 . The errors in the measurement of α and t are 1.2% and 1.6% , respectively. At t = 5 s , maximum percentage error in the energy is :

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​ d E = 3 α 2 d α e − βt + α 3 e − βt ( − β ) d t E d E ​ = α 3 d α ​ + ( − β ) d t E Δ E ​ = α 3Δ α ​ + β Δ t ​ (\%) Δ t = 1.6% × 5 = 8% % ( α 3Δ α ​ ) = 3 × 1.2% = 3.6% Putting values we get ⇒ 3.6 + 8 × 0.3 = 6%

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