Exam 1 - S09-1

# 05 20 solving it for s gives s 70 0000 05 1 e 1 5 536

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- 0 . 05 · 20 ). Solving it for S gives S = 70 , 000(0 . 05) / (1 - e - 1 ) 5 , 536 . 92 dollars per year. 15.) A. Making the substitution u = x 2 + 1 gives du = 2 xdx . Also when x = 0 the u = 1 and when x = then u = to. Thus we have Z 0 2 x ( x 2 + 1) 2 dx = Z 1 u - 2 du = - 1 u 1 = lim b →∞ - 1 u b 1 = lim b →∞ 1 - 1 b = 1 . B. The present value of the perpetual income stream produced by the highway is equal to: PV = Z 0 S ( t ) e - rt dt = Z 0 h 200 - 100 e - 0 . 01 t i e - 0 . 04 t dt = 200 Z 0 e - 0 . 04 t dt - 100 Z 0 e - 0 . 05 t dt = 200 e - 0 . 04 t - 0 . 04 0 - 100 e - 0 . 05 t - 0 . 05 0 = 200 0 . 04 - 100 0 . 05 = 3 , 000 million dollars . 2
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