The energy of a system varies as E(x,t)=x³ e ( − β t ) , e^(-βt), e ( − β t ) , where β=0.3 s⁻¹. Percentage error in x is 1.2% and percentage error in t is 1.6%. Find the maximum percentage error in E at t=5 s.

Question

G1 Physics · Accepted Answer

lnE=3lnx-βt. For maximum error, ΔE/E=3(Δx/x)+βΔt. Given Δx/x=1.2% and Δt/t=1.6%, at t=5 s, Δt=0.016×5=0.08 s. Thus percentage error=3(1.2%)+100(0.3)(0.08)%=3.6%+2.4%=6%.