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# Math 122 Exam 1 Study Guide MATH 122

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This 5 page Study Guide was uploaded by Sidney Strauss on Tuesday September 13, 2016. The Study Guide belongs to MATH 122 at University of South Carolina - Columbia taught by Francisco J. Blanco-Silva in Fall 2016. Since its upload, it has received 22 views. For similar materials see Calculus for Business Administration and Social Sciences in Math at University of South Carolina - Columbia.

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Date Created: 09/13/16

Math 122 Exam 1 Study Guide 1. In the equation V= f(s) which variable is dependent and which variable is independent? 2. Solid waste (W) generated In each city in the US is increasing. The waste generated in millions of tons was 348.4 in 2000 and 489.1 in 2006. Find the formula of the function using the equation of a line through these two points. 3. Gahanna’s population was 28,182 in 2000 and is growing by 961 people a year. a. Write the formula for Gahanna’s population in t years b. What will Gahanna’s population be in 2017? c. When will the population reach 41,000? 4. Year 1983 1984 1985 Height (in) 176 189 207 a) What is the change in height from 1983-1985? b) What is the average rate of change in height from 1983- 1985? 5. If the population of Gahanna increases by 1000 people what is the relative change in population if Gahanna’s population is 18,000? 6. A phone company is making and selling cell phones. The company’s fixed costs are 27,890 dollars and it costs them 24 dollars per cell phone made… a) What is the cost function? b) If the phone sells for 50 dollars each what is the revenue function? c) What is the profit function? d) When will the revenue equal the cost? 7. Which table represents supply and which represents demand? P 182 153 147 q 5 10 15 P 6 36 66 q 5 10 15 8. The initial amount of adrenaline in blood is 20 mg. Find the formula for the amount of blood in mg, t minutes after the amount of adrenaline in the blood is: a) Increasing by .3 mg per minute b) Decreasing by 6% per minute 9. The population of the world increased from 4.87 billion in 1981 to 5.57 billion in 1999. This increase continued at the same percent rate between 1999 and 2020. Express the population in billions as f(t) and use this to calculate the projected population. 10. The population of Ohio is 3.7 million people in 2000. In 2004 the population was 4.68 million. Assuming growth obeys the exponential laws find the formula as a function of t years after 2000. 11. Write the function P=20(1.7)^t in P=Poe^kt a) What was the continuous growth rate b) What was the annual growth rate? 12. Quality of ozone, Q, is decaying exponentially at a continuous rate of .65% per year. What is the half life? 13. A bank advertises an interest rate of 7% a year if you deposit 6,000 dollars. How much money is your account three years later? a) Annually? b) Continuously? 14. You win the lottery and are offered a choice between 1 million in four yearly installments of 250,000 each, starting now, or a lump sum of 900,000 dollars now. The interest rate is 4%. 15. What causes a vertical shift on a graph? 16. What causes a vertical stretch? 17. What causes reflection in respect to the x axis? 18. Does f(x+C) cause the graph to shift right or left?

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