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Unformatted text preview: Solution: We model the function H ( t ) as a sinusoidal function. The graph below shows temperature ( H ) as a function of the time t in hours. This is a phaseshifted cosine function with amplitude 15 and period 24. There is also a vertical shift of 85 units up. Since the period = 2 π B , we see that B = π 12 . H ( t ) = 85 + 15 cos ± π 12 ( t12) ² 4. Draw a graph of the function f ( x ) = arctan x . Label all important behavior. 2 5. Find a possible formula for the function g ( x ) whose graph is given below. Solution: Notice that there are three roots (zeros) of g ( x ): 3, 0, and 4. Hence, g ( x ) = k ( x + 3) x ( x4) for some constant k . We can determine k by using the fact that (2 , 3) is on the graph: 3 = g (2) = k (2 + 3)(2)(24) 3 =20 k k = 320 Hence, g ( x ) =3 20 ( x + 3) x ( x4) 3...
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 Spring '08
 KENNEDY
 Math, Calculus, Exponential Function, Derivative, Natural logarithm, Euler's formula, Exponentials

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