M408D SPRING 2015 HOMEWORK #5 - cheatham (sc36975) HW05 um...

  • University of Texas
  • M M408D
  • Test Prep
  • TeddyMcDeez
  • 7
  • 67% (3) 2 out of 3 people found this document helpful

This preview shows page 1 - 3 out of 7 pages.

cheatham (sc36975) – HW05 – um – (53890)1Thisprint-outshouldhave15questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.001 (part 1 of 3) 10.0 pointsAn initial deposit of $Pis made into anaccount that earns 8% interest compoundedcontinuously. Money is then withdrawn at aconstant rate of $5000 per year.Set up the differential equation for theamountA=A(t) (in thousands of dollars)in the account aftertyears.1.dAdt= 8A52.dAdt= 8A+ 53.dAdt=A54.dAdt= 0.08A5correct5.dAdt= 0.08A+ 5Explanation:The interest earned by the account will in-crease the balance at a rate of 0.08Awhile theconstant withdrawals of $5000 will reduce thebalance at a constant rate 5, the account bal-anceA(t), expressed in thousands of dollars,will satisfy the equationdAdt= 0.08A5.002 (part 2 of 3) 10.0 pointsSolve the differential equation in part 1.1.A(t) = 62.5 +P1000+ 62.5e0.08t2.A(t) = 62.5 +62.5P1000e0.08t3.A(t) = 62.5 +P100062.5e0.08tcor-rect4.A(t) = 0.625 +P10000.625e0.08t5.A(t) =P100062.5e0.08tExplanation:After rewriting the differential equation inpart 1 asdAdt0.08A=5,it can be solved by using the integrating factorμ(t) =e0.08dt=e0.08t.In this casee0.08tdAdt0.08Ae0.08t=ddtAe0.08t=5e0.08t,soA(t) =e0.08tC+ 62.5e0.08t=Ce0.08t+ 62.5.withCan arbitrary constant.The initialdeposit determinesCsinceA(0) =P1000=C=P100062.5.ThusA(t) = 62.5 +P100062.5e0.08t.003 (part 3 of 3) 10.0 pointsIf the account balance becomes zero after8 years, what was the amount of the initialdeposit $P? (This value ofPis often calledthePresent Valueof the regular withdrawals$5000 over a period ofnyears.)1.$34416
cheatham (sc36975) – HW05 – um – (53890)22.$365763.$267994.$29544correct5.$32077Explanation:Since the balance becomes zero after 8years,0 = 62.5 +P100062.5e0.64.Solving forPwe see thatP= 62500 1e0.64$29544.00410.0 pointsDiana is sick in hospital with a severe bac-terial infection.She is to be fed antibioticsintravenously at a constant infusion rate, andthe doctor knows that the anti-biotic will beeliminated from the bloodstream at a rateproportional to the amounty(t) present inthe bloodstream at timet. If the half-life ofthe anti-biotic in the bloodstream is 2 hours,what rate of infusion should he prescribe tomaintain a long-term amount of 390 mgs in

Upload your study docs or become a

Course Hero member to access this document

Upload your study docs or become a

Course Hero member to access this document

End of preview. Want to read all 7 pages?

Upload your study docs or become a

Course Hero member to access this document

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture