A physical quantity Z as a function of time is given as Z(t)=A32e–kt, where k=0.1s–1. The measurement of A has an error of 2.00%. If the error in the measurement of time is 1.25%, then the percentage error in the value of Z(t) at t=10s would be
A
2.50%
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B
3.50%
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C
3.75%
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D
4.25%
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Solution
The correct option is D4.25% lnZ=32lnA−kt ΔZZ=32ΔAA+ktΔtt=32×2+1.25=4.25%.