Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2004 / Paper 2 / 9 / b / i / Solution

Use the fixed exponents $p,q$ in the original PDF. Assume positive $a,b$ so arbitrary real powers and a relative change are defined. Set $h=k/100$. With $b$ fixed, the exact new-to-old ratio is $(1+h{)}^p$. The binomial series, or the one-variable case of the second-order relative change of a monomial, givesTherefore the approximate percentage change through second order isFor negative $k$ this same signed expression describes a decrease.