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# ALGEBRA WITH APPL MATH 111

UW
GPA 3.76

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
10
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 10 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 Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/192092/math-111-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15
1L W Sawmg 1km 7mm Mong Kon Mo August 13 2007 Course Website httpwwwma lhwashimg loneduNmkmoma39lh i 1 u Sittion There are two accounts Account A 10 annually compounded continuously Account B 11 annually compounded quarterly Q If we deposit 1000 now when will there be 1200 in the account Account A The balance in the account after t years is At Pe 100052010 So we have 1200 100020lot 12 e010 To solve this equation we need to know the power that e must be raised to to get 12 Te Natural Logarithm If equot y then we say that x is the natural logarithm of y and write 1ny x This means that 1ny is the power you must raise e to to get y Laws of Logarithms 0 If a b then 111a lnb e 111ab blna Caution h1ab 7 bna 0 1116 1 9 h1ab lnalnb Caution lnab 7 111a 11b 9 In 111a 711119 111W 11117 Caution lna 7 b 7 Math 111 Acunt A So we have 12 010 11112 lneo3910t 11112 010t11e 11112 010t 7 11112 7 010 z 182 years Account B The balance in the account after t years is 011 4 4t Bt1000 1T 100010275 So we have 1200 1000102754t 12 10275 11112 h1102754t 11112 4t1110275 t 11112 4n10275 z 168 years Another Question Q How long will it take to double your balance Note It suffices to find how long it takes to double your principal For Account A For Account B 2P 1052010t 2P 10002754t 2 eOW 2 102754t 1112 111e010t 1112 111102754t 1112 010 lne 1112 4t 11110275 1112 7 1112 n t7 4n10275 z 693 years z 639 years Another Question Q An account pays r x 100 annual interest compounded continuously and it takes 73 years to quadruple the balance Find r The balance in the account after t years is At Pequot So A73 105273r 4P 73r 4 73r 1n4 ln4 r 73 x 01899 Another Question Q An account pays r x 100 annual interest compounded semiannually and it takes 73 years to quadruple the balance Find r 2t The balance in the account after t years is At P lt1 So 273 A73 P 1 lt1 gt1454 r 1 1 4145 2 ltgt r2471671 4P x 01992 The Moral It the variable you are solving for appears in the exponent then you need to use the natural logarithm It the variable you are solving for appears in the base then you DON39T need to use the natural logarithm

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