The production of a company has ups and downs | vedclass

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(C) Let the initial production in the year $1998$ be $P$.The production pattern is: increase by $15\%$ for two years,then decrease by $10\%$ in the th

Vedclass · Accepted Answer

$37\%$ increase

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(C) Let the initial production in the year $1998$ be $P$.The production pattern is: increase by $15\%$ for two years,then decrease by $10\%$ in the third year.For the years $1998$ to $2002$ (a span of $4$ years),the production changes as follows:Year $1$: Increase by $15\% = P 	imes 1.15$Year $2$: Increase by $15\% = (P 	imes 1.15) 	imes 1.15$Year $3$: Decrease by $10\% = (P 	imes 1.15 	imes 1.15) 	imes 0.90$Year $4$: Increase by $15\% = (P 	imes 1.15 	imes 1.15 	imes 0.90) 	imes 1.15$Resultant production $= P 	imes 1.15 	imes 1.15 	imes 0.90 	imes 1.15$$= P 	imes (1.15)^3 	imes 0.90$$= P 	imes 1.520875 	imes 0.90$$= P 	imes 1.3687875$Percentage change $= (1.3687875 - 1) 	imes 100 = 36.87875\% \approx 37\%$ increase.

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