Math111i_Quiz7_Solutions

# Math111i_Quiz7_Solutions - the investment doubles(Use log...

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Math 111I Sec 001 Quiz 7 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. Fully expand the logarithm. ln( m 2 n 4 ) Solutions. The solution is given by the following computation. ln( m 2 n 4 ) = ln( n 2 ) + ln( m 4 ) = 2 ln( n ) + 4 ln( m ) 2. Fully simplify the expressions (a) 6 ln( x ) + 4 ln( y ) - 3 ln( z ) (b) 6 log( x ) + 4 log( y ) - 3 log( z ) Solutions. (a) The solution is given by the following computation. 6 ln( x ) + 4 ln( y ) - 3 ln( z ) = ln( x 6 ) + ln( y 4 ) - ln( z 3 ) = ln( x 6 y 4 ) - ln( z 3 ) = ln ± x 6 y 4 z 3 ² (b) The logic for this problem is exactly the same just replacing ln with log. So the answer follows as 6 log( x ) + 4 log( y ) - 3 log( z ) = log ± x 6 y 4 z 3 ² . 3. The function V ( t ) = 5500 e 0 . 06 t , gives the value V ( t ), of an investment t years after the initial investment. How many years until the worth of

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Unformatted text preview: the investment doubles? (Use log or ln to ﬁnd the answer). Math 111I Sec 001 Quiz 7 Solutions Solutions. We want to ﬁnd the value of t that gives us 2 times our initial investment. Well the initial investment is \$5500, and twice that is \$11000. So we want to ﬁnd t such that V ( t ) = 11000. Now that is the same thing as saying solve the equation 11000 = 5500 e . 06 t for t. So our solution follows as 11000 = 5500 e . 06 t 11000 5500 = e . 06 t 2 = e . 06 t ln(2) = ln( e . 06 t ) ln(2) = 0 . 06 t ln(2) . 06 = t ≈ 11 . 55 4. Solve the equation for t 45 e-. 17 t = 25 . Solutions. The solution is given by the following computation. 45 e-. 17 t = 25 e-. 17 t = 25 45 ln( e-. 17 t ) = ln ± 5 9 ²-. 17 t = ln ± 5 9 ² t = ln ( 5 9 )-. 17 ≈ 3 . 458...
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Math111i_Quiz7_Solutions - the investment doubles(Use log...

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