MAC_2233_SummerB_2017_Quiz_1_Solutions.pdf

MAC_2233_SummerB_2017_Quiz_1_Solutions.pdf

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MAC 2233 - QUIZ 1 1. June 30, 2017 Problem 1.1. The following table shows the gasoline consumption of a car, Y (in gallons), as a function of the distance traveled, X (in miles). Find a function of X that describes this dependence, Y = f ( X ) . Then find the inverse function X = g ( Y ) , and compute g (12) . What is the meaning of the value computed? X = 100 X = 150 X = 450 Y 3 4.5 13.5 Since the ratios of changes in Y divided by changes in X are all constant, Y 2 - Y 1 X 2 - X 1 = 4 . 5 150 = 13 . 5 450 = 3 100 m, we are looking for a linear function, that is Y = f ( X ) = mX + n = 3 100 X + n Setting Y = 3 , X = 100, we get n = 0, so the function is f ( X ) = 0 . 03 · X . To find the inverse, solve Y = 0 . 03 · X for X , and obtain X = g ( Y ) = 100 3 Y . Setting Y = 12, we compute g (12) = 400, and the interpretation is that the car must travel 400 miles in order for the total gas consumption to equal 12 gallons. Problem 1.2. The mutual fund A has a cost-per-share of 0 . 02$ , and a fixed annual fee of 10$ . The fund B has a cost-per-share of 0 . 03$ , and a fixed annual fee of 5$ . Fund C has a flat rate of 20.05 $ . For what number of shares is it more expensive to hold the fund B than the fund
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