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# ALGEBRA WITH APPL MATH 111

UW

GPA 3.76

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This 2 page Class Notes was uploaded by Addison Beer on Wednesday September 9, 2015. The Class Notes belongs to MATH 111 at University of Washington taught by Alexandra Nichifor in Fall. Since its upload, it has received 21 views. For similar materials see /class/192058/math-111-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15

Math 111 Some Skills to Review for the Final First look at the previous review files for Midterrns 1 and 2 Besides the material from the two midterrns review the following newer concepts and skills 1 Sequences o How to determine if a given sequence is additive multiplicative or neither 0 Know how to nd and use recursive formulas for additive and multiplicative sequences EX Ak1 Ak 5 or Mk1 5 Mk or Mk3 53 Mk 0 Be able to determine explicit formulas for additive and multiplicative sequences EX AkA05k or MkM05k 0 Understand the relationship between multiplier m and proportionate change p Speci cally understand the two ways to get Mk1 from Mk o Mk1m Mk think bacteria population 0 Mk1Mk1 r think interest in an account 0 Know how to compute proportionate change and percent change over a given time period New Old 1 chan e gtlt100 P quot7 Old 0 g P 0 2 Simple Interest interest is applied to the principal P only The account balance after t interest periods at a rate ofr X 100 is A t P 1rt 3 Compounded Interest Formulas interest is applied to the entire balance each time CAF where P initial quantity k of compounding and r rate per compounding period in decimal form Useful in problems with accounts compounded annually or with strange compounding periods nt 0 The general CAF discretely compounded interest At P 1 1 n Pinitial amount ryearly rate in decimal form n of compoundings a year and tof years Use this if you re given an annual rate and an indication of how many times a year the interest is compounded eg monthly Given enough information you should be able to solve for a At lture values b AOP present value c Interest rate r d of years t requires natural log be able to use it 0 Continuous Compounding Given enough information you should be able to solve for a At lture values b AOP present value c rate r requires natural log d of years t requires natural log be able to use it quotAI A0 Understand that the annual percentage yield APY s the percentage change in the balance of an account over a oneyear period and that it s greater than or equal to the nominal annual interest rate listed by the bank 0 Know how to compute the APY m 1 X 100 1 X 100 Math 111 Skills to Review for the Final Look at the reviews for Midterms 1 and 2 Besides the material from the two midterms review the following skills 1 Sequences 0 How to tell if a given sequence is additive multiplicative or neither 0 Know how to find and use recursive formulas for additive and multiplicative sequences EX Ak1 Ak 5 or Mk1 5 Mk or Mk3 53Mk Be able to determine explicit formulas for additive and multiplicative sequences Understand the relationship between multiplier m and proportionate change p Specifically understand the two ways to get Mk1 from Mk o Mk1m Mk think bacteria population 0 Mk1Mk p Mk think interest in an account 0 Know how to compute proportionate and change over a given time period 2 Simple Interest interest is applied to the principal P only The account balance after t interest periods at a rate of r x 100 is AtP1rt 3 Compounded Interest Formulas interest is applied to the entire balance each time 0 CAP where P initial quantity k of compoundings and rprop change Useful in population problems or problems with accounts compounded annually or with strange compounding periods 0 The general CAF discretely compounded interest At P 1 1 n Pzinitial amount ryearly rate in decimal form n of compoundings a year and tof years Use this if you re given an annual rate and an indication of how many times a year the interest is compounded eg monthly Given enough information you should be able to solve for a At future values b A0P present value c Interest rate r d of years t requires natural log be able to use it 0 Continuous Compounding Given enough information you should be able to solve for a At future values b A0P present value c rate r requires natural log d of years t requires natural log be able to use it A1 0 Knowhowtocomputethe APYm 1gtlt1000 gtlt100 A0 Understand that the APY is the percentage change in the balance of an account over a one year period and that it s greater than or equal to the nominal annual interest rate listed by the bank

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