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1. In each part below a sequence of numbers is given. For each sequence decide whether or not it is an example of (A) arithmetic growth, (Q) quadratic growth, or (N) neither of these. Li a) 25.0, 30.0, 36.0, 43.2, 51.84,... “ah neither - because neither the first nor second differences are constant (or close to it). b) 5.0, 6.7, 8.4, 10.1, 11.8,... linear - because the first differences are constant ead d=1.7 ©) 11.0, 11.5, 12.0, 12.5, 14.0, 16.0, 18.5,... neither - because neither the first nor second differences are constant (or close to it). 2. The fuel efficiency of the average car can be modeled with the following quadratic equation: F(v) = -.018v’+1.47v+3. 4, where v = speed of the car in mph. aE a) ~=6©What speed will yield the maximum fuel efficiency? The maximum will occur at the vertex of the parabola (at the center line). This is where the speed is v = -b/2a = -1.47/(-.036) = 40.83 mph b) What is the maximum fuel efficiency? 5 The maximum fuel efficiency occurs when you plug 40.83 mph in for the speed: F(40.83) = -.018(40.83)? + 1.47(40.83)+3.4 = 33.41 mpg 3. The initial term of a sequence J is 50. To get the next term, take the previous value, multiply by -1, and then add 75. Write the difference equation for this sequence using correct notation. Then find the first 5 terms of the sequence. 150 - so yes, we need to publish an alert. 13. Determine the orientation (up or down); y- intercept; centerline, vertex (max. or min.), and x-intercepts of the following parabolas: Ne a a) y=—4x7 43x42 opens down y-intercept = (0,2) center line: x = 3/8 maximum: (3/8, 2.5625) x-intercepts: (-.425,0), (1.175, 0) 13. Determine the orientation (up or down); y- intercept; centerline, vertex (max. or min.), and x-intercepts of the following parabolas: Me 3E c)y=xt+4xt+4 opens up y-intercept = (0, 4) center line: x = -2 minimum: (-2, 0) x-intercept: (-2, 0) 14. Three quadratic equations are given below. The graph of one of these has exactly two x-intercepts, one graph has exactly one x-intercept, and the remaining graph has no x-intercepts. Identify the number of x-intercepts in each case and give a brief reason for your answer. It is not necessary for you to actually find the x-intercepts in any case. a) y= 3x7+6x412 ME a There are no x-intercepts because b?-dac is negative. 
