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Test1 - MA303 TEST 1 NAME Tuesday Sept 18 2007 SHOW YOUR...

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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 (b) How many months will it take before Fred has withdrawn all his money?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! 3-2 Ail/9+3 )4 =3 5000 o = C -H00000 9 (3-5” .49: .. a) -:_ _ /00000 fl- __ -1? tr. [MA 303 Tq+ll @D _._-3 gfigqch MAGEELHW______-_____ (5. Am =Cff+IJA2 «a? 5': kH _—- --———il'——-Qc¢‘;-:m —2—« (16ng @fl):—~—/&+L~ ;~§é—1-—é/:—A 14E: ::-_m——C—FT-j? Z17) l2?..21.+§-_,_.__.._-___.__.. "WW JXLEXL/ 2_ KL?“ t/r KF/f Ljvéafim _, __.~_. _--_;[email protected]) 4&443 +£flf._qu—:T;iéflrw96f=—~駔£: “ “7f“ Zczr—m W “52%;52‘2i‘23li?” Lit" - (a)~ _Qf_¢+1:m%,L24: .__.-.—._ w.._. m... _._...___._ ..... .____.‘..__‘ H..- A ).._._.. .__._ ._.____._..__._,..._ wak 4 mflyq; 2,) ( Lt: 14.2 L +9.._L_~.,V):-W_::_: ’I + 16 ,, .L(/_%:)_._L;—___Ui3;£fé_tl_«_c : ,f’,i3¢(;f%_téi ...
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