The energy of a system is E(t)=A²exp(−αt), with α=0.2 s⁻¹. A has a 1.25% error and the measured time has a 1.50% error. Find the percentage error in E at t=5 s, rounded to the nearest integer.

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G1 Physics · Accepted Answer

lnE = 2lnA−αt, so maximum fractional error is ΔE/E = 2ΔA/A + αΔt. Here ΔA/A=1.25%, and Δt=1.5% of 5 s =0.075 s. Thus error =2.5% +0.2×0.075×100%=4.0%. Answer: 4.