The energy of a system as a function of time `t` is given as `E(t) = A^(2) exp(-at), where alpha = 0.2 s^(-1)`. The measurement of `A` has an error of `1.25%` . If the error in the measurement of time is `1.50%` , the percentage error in the value of `E(t) at t = 5 s` is

Explanation

`E(t) = A^(2) e^(-at)` ltbr. `alpha = 0.2s^(-1)`
`(dA)/(A) = 1.25%`
`(dt)/(t) = 1.50%`
`(dE)/(E) = ?`
`log E =2 log A - alphat`
`(dE)/(E) = +- 2 (dA)/(A) +- alphadt`
`=+-2 (1.25) +- 0.27 (7.5)`
`=+- 2.5 +- 1.5`
`= +- 4%` .