Answer :

Given pv1.4 = constant and the decrease in v is.


Hence, we have


Δv = –0.005v


We have pv1.4 = constant


Taking log on both sides, we get


log(pv1.4) = log(constant)


log p + log v1.4 = 0 [ log(ab) = log a + log b]


log p + 1.4 log v = 0 [ log(am) = m log a]


On differentiating both sides with respect to v, we get




We know






Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as



Here, and Δv = –0.005v



Δp = (–1.4p)(–0.005)


Δp = 0.007p


The percentage error is,



Error = 0.007 × 100%


Error = 0.7%


Thus, the error in p corresponding to the decrease in v is 0.7%.


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