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The energy of a system as a function of time t is given as E(t) =A^2 exp(-at), where a=0.2 s^-1. The measurement of A has an error of 1.25%. If theerror in the measurement of time is 1.50%, the percentage error in thevalue of E(t) at t5 sec is

Question

The energy of a system as a function of time t is given as E(t) =A^2 exp(-at), where a=0.2 s^-1. The measurement of A has an error of 1.25%. If theerror in the measurement of time is 1.50%, the percentage error in thevalue of E(t) at t5 sec is

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Solution

The percentage error in a given quantity is the sum of the percentage errors in the quantities it depends on.

In this case, the energy E(t) depends on A and t.

The percentage error in A is given as 1.25%.

The percentage error in t is given as 1.50%.

Therefore, the total percentage error in E(t) is the sum of these, which is 1.25% + 1.50% = 2.75%.

So, the percentage error in the value of E(t) at t=5 sec is 2.75%.

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