Math111i_Quiz8_Solutions

Math111i_Quiz8_Solutions - = e 12 So we have that r = a-1 =...

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Math 111I Sec 001 Quiz 8 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. Convert the function f ( t ) = 9300(1 . 74) t to the form f ( t ) = Ce kt (that is ﬁnd C and k for the function f ( t ) = Ce kt ). Solutions. We begin by noticing that for 9300(1 . 74) t = Ce kt we must have that C = 9300, and further we must have that 1 . 74 = e k . Thus, we solve this equation for k , 1 . 74 = e k ln(1 . 74) = ln( e k ) ln(1 . 74) = k 0 . 554 So our equation follows as f ( t ) = 9300 e 0 . 554 t . 2. (This problem is to determine how well you remember the deﬁnitions that have been given). A continuous growth rate of 12% corresponds to what growth rate? ( Hint: The growth rate and growth factor are very closely related). Solutions. The deﬁnition of continuous growth rate tells us that 0 . 12 = 12% = k in the function f ( t ) = Ce kt . The deﬁnition for the growth rate is r such that a = 1 + r in the equation f ( t ) = Ca t . So we begin by ﬁnding a so that a

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Unformatted text preview: = e . 12 . So we have that r = a-1 = e . 12-1 = 0 . 1275 So we see that the growth rate is 12 . 75%. 3. Expand the following expression fully using the rules of logarithms, log ( √-5 a + 4 ) . Math 111I Sec 001 Quiz 8 Solutions. The solution is given by the following computation log ( √-5 a + 4 ) = log ± (-5 a + 4) 1 / 2 ² = 1 2 log(-5 a + 4) . Now we cannot proceed any further because we have no rule for addition inside the parentheses for the log function. 4. Expand the following expression fully using the rules of logarithms, ln ± (-5 a + 6) √ 2 a + 6 ² Solutions. The solution is given by the following computation, ln ± (-5 a + 6) √ 2 a + 6 ² = ln(-5 a + 6) + ln ± √ 2 a + 6 ² = ln(-5 a + 6) + ln ± (2 a + 6) 1 / 2 ² = ln(-5 a + 6) + 1 2 ln(2 a + 6) . And again we cannot continue because we have no rules for logs that deal with addition inside the parentheses....
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This note was uploaded on 02/16/2011 for the course MATH 111 taught by Professor Hitchcock during the Fall '08 term at South Carolina.

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Math111i_Quiz8_Solutions - = e 12 So we have that r = a-1 =...

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