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exam2solns

# exam2solns - Math 115 Second Midterm Name EXAM SOLUTIONS...

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Math 115 / Exam 2 (November 15, 2011) page 2 1 . [9 points] Let U = f ( t ) give the number of Facebook users in millions in year t . Suppose f (2005) = 5 . 5 and f (2005) = 4 . 9. For this problem assume that f ( t ) is strictly increasing. a . [4 points] Find and interpret, in practical terms, f 1 (5 . 5). Solution: The year in which there were 5.5 million Facebook users was 2005. f 1 (5 . 5) = 2005 (year) b . [5 points] Showing work, evaluate ( f 1 ) (5 . 5). Interpret your answer in practical terms. Solution: ( f 1 ) (5 . 5) = 1 / ( f ( f 1 (5 . 5)) = 1 /f (2005) = 1 / 4 . 9 . When the number of Facebook users was 5.5 million, in 1/4.9 ( 0.2) years the number of Facebook users will have increased by approximately 1 million users. ( f 1 ) (5 . 5) = 1 / 4 . 9 years per million users 2 . [8 points] Recall the function T ( x ) that took the number of followers (in millions) of a Twitter user and returned a value from 0 to 10 called the user’s Twitter celebrity index. The derivative of T ( x ) is given by the function T ( x ) = 1532 . 5 · (0 . 6) x (5 + 60(0 . 6) x ) 2 . a . [4 points] If T (3) = 1 . 56, compute the local linearization of T ( x ) near x = 3. Solution: The formula for the local linearization for a function f ( x ) near a point x = a is L ( x ) = f ( a ) + f ( a )( x - a ) .
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exam2solns - Math 115 Second Midterm Name EXAM SOLUTIONS...

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