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Math111i_Quiz6_Solutions

# Math111i_Quiz6_Solutions - (c As x → ∞ which function(s...

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Math 111I Sec 001 Quiz 6 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. Which of the following functions has the steepest graph? F ( x ) = 75(1 . 8) x , G ( x ) = 75(0 . 9) x , H ( x ) = 75(1 . 8) - x Solutions. This is a bad problem. But 5.4.13 in the book is not a bad problem, why? 2. Construct an exponential function f ( x ) given the following information f (0) = 3 and f (4) = 261 . Solutions. We begin by noticing that f (0) = C · a 0 = C = 3 . So our function becomes f ( x ) = 3 · a x . So then we observe that f (4) = 3 a 4 = 261 a 4 = 261 3 a 4 = 87 a = (87) 1 / 4 3 . 05 Thus we have that f ( x ) = 3(3 . 05) x . 3. Given the following functions f ( x ) = 5(3) x g ( x ) = 100(0 . 9) x h ( x ) = 5 + 3 x k ( x ) = 100 - 9 x (a) As x → ∞ , which function(s) approach 0?

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Math 111I Sec 001 Quiz 6 (b) As x → -∞ , which function(s) approach 0?
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Unformatted text preview: (c) As x → ∞ which function(s) approach ∞ ? Solutions. (a) The only function that approaches 0 as x → ∞ is g ( x ). (b) The only function that approaches 0 as x → -∞ is f ( x ). (c) There are two functions that approach ∞ as x → ∞ and those are f ( x ) and h ( x ). 4. For an exponential function, f ( x ) = C · a x , where x is measured in months and f (2) = 13 and f (11) = 48 . Find (a) The 9-month growth factor. (b) The monthly growth factor. Solutions. (a) The 9-month growth factor happens over the 9 month period x = 2 to x = 11, which we have values for. So we see that a 9 months = 48 13 ≈ 3 . 69 . (b) To ﬁnd the one month growth factor we have that a 1 month = ( a 9 months ) 1 / 9 ≈ (3 . 69) 1 / 9 ≈ 1 . 16 ....
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