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Unformatted text preview: MA303 TEST 1 NAME
Tuesday, Sept. 18, 2007 SHOW YOUR WORK. CORRECT WORK AND A CORRECT ANSWER ARE NEEDED
TO OBTAIN FULL CREDIT. 1.(30%) Use homogeneous and particular solutions to solve each equation. (a) AE: $k+1=2$k+3k+1 for [$20 and IC: 330:1. (b) AE: mk+1=xk+1+k for 1:20 and IC’: xo=1. 2.(20%) Fred inherits $50,000 and deposits it in the bank at an annual interest rate
of 12%, compounded monthly. He intends to withdraw $1000 per month. (a) Write a difference equation with initial condition for risk, the amount of money
left in the bank at the end of the k—th month after interest has accrued
and the withdrawal made. Find its solution. (b) How many months will it take before Fred has withdrawn all his money? (c) With the same interest rate and monthly withdrawal, what is the minimum
amount of money Fred must inherit so that he never runs out of money?
Explain. 3.(12%) If an insect population doubles every season, how many seasons will it take for
the population to reach 256 insects starting from 2 insects? Write a difference
equation that describes this process. 4.(6%) By direct substitution show that an, = k2 satisﬁes the difference equation: $k+2=2$k+1”‘$k+2 k20 5.(20%) Use the method of undetermined coefﬁcients to write the appropriate form of
a particular solution for each equation. Do n_ot evaluate the undetermined coefﬁcients.
(a) $k+1 = 31L}, + 3 ' 2k (b) $k+1 = 21)}: — 2—k
(C) $194.1 = 217]; + 2162 (d) 2$k+1 = 2112}: + k2 (3.(12%) Find each complex number in the form a + bi. (a) 4i(2—i)(1+z’) (b) 15:2; ¢_M__7_W
"‘(Pl :‘hL ‘A ‘ H" +3! 32 Ail/9+3 )4 =3 5000 o = C H00000 9 (35” .49: ..
a) :_ _ /00000
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 Spring '08
 Selgrade

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