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124exam1solutions

# 124exam1solutions - Math 124 Exam 1 Sept 14 2006 Name...

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Math 124 Exam 1 Sept. 14, 2006 Name Directions 1. SHOW YOUR WORK and be thorough in your solutions. Partial credit will only be given for work shown. 2. Any numerical answers should be left in exact form, i.e, no decimal approximations. 3. You may use calculators. Good luck! 1. One of the following tables of data is linear and one is exponential. Say which is which and give an equation that best fits each table. Solution: A linear function will have constant differences in y with constant changes in x . An exponential function will have constant ratios in y with constant changes in x . Notice that in the first table the ratios of y values is constant- approx. 0 . 84. We use y = Ca x . Since y = 3 . 12 when x = 0, we see that C = 3 . 12. Using the point (1 . 00 , 2 . 20), we see that 2 . 2 = (3 . 12) a 1 , hence a = 2 . 2 3 . 12 . This gives y = 3 . 12 2 . 2 3 . 12 x The second table, being linear, has a slope of m = 3 . 94 - 2 . 71 0 . 5 = 2 . 46. Using y - y 1 = m ( x - x 1 ), we have y - 2 . 71 = 2 . 46( x - 0), or y = 2 . 46 x + 2 . 71 . 2. From the graph of y = f ( t ) below, describe the domain and range of f ( t ). In a sentence, apply the general definition of “function” to explain why you think that the given curve is in fact a function. Solution: The domain is simply the input values for the function, roughly [1989 , 1992] The range is the possible output vales of the function, roughly [2800 , 4100] The curve is a function since every input value has at most one output.

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