## Y

PCY" p

G - ~ (to PCY)« -7-(In V)--7-(In/*) - O.OI5-OQ25 - -0.01 - -1% ai ai di

Per capita incomc i\ falling by 1 percent a year.

9.27. A country exports two goodv copper c and bananas b. where earnings in terms of million dollars are r - eft«) - •» b - b{ib) » I

If c grow* by 10 percent and b by 20 percent, what is the rale of growth of export earnings £?

From the rules of derivatives in Section 9.1.3.

Then substituting the given values.

G| —^(0.10) - —Í-(0l2O) - 7(0.10) + j(0 20) »0.12 <k 12% 4*1 4-1 5 5

Iln growth rate of a function involving the sum of other functions is the sum of the weighted average of the growth of the other functions

9.2K. A company derives 70 percent of its revenue from bathing suits. 20 percent from bathing caps and 10 percent from bathing slippers. If revenues from bathing suits increase by 15 percent, from caps by 5 percent, and from slippers by 4 percent, what is the rate »if growth ol total revenue?

Gm - 0 70(0 15) 4 0.20(005) + O.HMO.OI) - 0.105 ♦ 0.01 ♦ O.tVM - 0.119 or 11.9*

9.29. Find lhe relative growth rate (i of vales al / « 4. given S(/) - 100.000^ *vT

hi5(0 - In IOOjQOO ♦ lne*,vi - In 1(10.000 * 03Vf Take the derivative jnd recall that 05 Vf « 0 V \