Exam_1_Solns precalc

# Exam_1_Solns precalc - MATH 105 FIRST MIDTERM EXAM...

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2 1. (2 points each) For each question, circle either increasing or decreasing. Also, circle either linear, concave down, or concave up. You should circle only one item per row. (a) Jared runs cross country. At the beginning of a race, he has a lot of energy. As the race starts off he loses energy slowly, but as the race goes on, he loses energy more and more rapidly. Is Jared’s energy an increasing or decreasing function of time, and is it linear, concave up, or concave down? increasing decreasing linear concave up concave down (b) An aircraft is ascending at a smaller and smaller rate. Is the aircraft’s altitude as a function of time increasing or decreasing, and is it linear, concave up, or concave down? increasing decreasing linear concave up concave down (c) In a certain country, people are being born at a greater rate than they are dying. However, both the birth and the death rates are constant. Is the population of that country increasing or decreasing, and is it linear, concave up, or concave down? increasing decreasing linear concave up concave down (d) A function is given by x 0 2 4 6 f ( x ) -15 -12 - 8 -3 Based on the data, do you expect this function is increasing or decreasing, and do you expect it is linear, concave up, or concave down? increasing decreasing linear concave up concave down
3 2. The graph below depicts four linear functions, P , Q , R , and S . The functions y 1 , y 2 , y 3 , and y 4 are the equations of the four lines, and the constants a, b, c > 0 are all positive.

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