Math111i_GroupQuiz6_Solutions

# Math111i_GroupQuiz6_Solutions - Math 111I Sec 001 Name...

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Math 111I Sec 001 Group Quiz 6 Solutions Name Directions: Read each question carefully and answer in the space pro- vided. The use of calculators is allowed, but not necessary. There are 10 points possible. To receive partial credit on any problem work must be shown. 1. Simplify the following expression using the rules for logarithms. Ex- press your answer as a single logarithm 4 log( A ) + 2 log( B ) - 4 log( C ) Soluitons. The computation follows as 4 log( A ) + 2 log( B ) - 4 log( C ) = log( A 4 ) + log( B 2 ) - log( C 4 ) = log( A 4 · B 2 ) - log( C 4 ) = log A 4 · B 2 C 4 . 2. Expand the following expression using rules of logarithms and expo- nents. log m 2 n 5 p 6 ! Solutions. The computation follows as log m 2 n 5 p 6 ! = log m 2 / 2 · n 5 / 2 p 6 = log( m · n 5 / 2 ) - log( p 6 ) = log( m ) + log( n 5 / 2 ) - log( p 6 ) = log( m ) + 5 2 log( n ) - 6 log( p )

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Math 111I Sec 001 Group Quiz 6 Solutions 3. Alice invests \$18,000 in an account offering 5.5% interest compounded daily (365 times per year). How many years until the account value reaches \$40,000? Solutions. The formula we use here is the n -times compounding per year which is P ( t ) = P 0 1 + r n n · t , where from the problem we have that P 0 = 18000, n = 365, and r = 5 . 5% = 0 . 055. So our equation becomes P ( t ) = 18000 1 + 0 . 055
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