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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11.6%

8.4%

answer is C.

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Detailed Solution

$\begin{array}{l} α^{3} e^{- βt} \\ \ln E = 3 \ln α - βt \\ {(\frac{dE}{E})}_{max} = \frac{3 dα}{α} + β \frac{dt}{t} \times t \end{array}$
= 3 × 1.2% + (0.3 × 1.6 × 5)%
= 6%

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