410 CHAPTER 3 Polynomial and Rational Functions 77. Average Cost A manufacturer determines that the average daily cost (in dollars) of producing x units of a certain commodity is given by the function C1x2 = 100x + 1500 x , x 70, where $1500 is the fixed cost and $100 is the variable cost. For what values of x will the average cost be less than $110? 78. Drug Level in the Bloodstream When a certain drug is taken orally, the amount of the drug (in milligrams) in the bloodstream after t hours is given by the function ƒ1t2 = 100t 1 + t2 , t 70. For what values of t will the amount of drug in the bloodstream be at least 40 mg? These summary exercises provide practice with solving equations and inequalities. Concept Check Use the graph of the function to solve each equation or inequality. Summary Exercises on Solving Equations and Inequalities 1. (a) ƒ1x2 70 (b) ƒ1x2 … 0 x y y 5 f(x) 1 1 –1 0 2. (a) ƒ1x2 60 (b) ƒ1x2 70 x y 1 –1 –1 0 y 5 f(x) 3. (a) ƒ1x2 = 0 (b) ƒ1x2 70 x y 5 –5 10 2 –10 0 y 5 f(x) –2 4. (a) ƒ1x2 = 0 (b) ƒ1x2 … 0 x y 2 3 2 4 –6 6 0 1 –2 –4 y 5 f(x) Solve each equation or inequality. Use interval notation where appropriate. 5. 5x + 8 -2 = 2x - 10 6. 1 5 x + 0.25 x = 1 2 x - 1 7. x2 + x - 3 = 0 8. 2x2 + x + 1 = 0 9. 22x - 5 - 2x - 3 = 1 10. 3 = 2x + 2 + 2x - 1 11. x3 - 5x2 + 6x x2 = 0 12. x3 - 2x2 + x x2 - 1 = 0 13. x2/3 + 1 2 = 3 4 14. 27 - 1x - 423/2 = 0 15. 1x - 52-4 - 131x - 52-2 = -36 16. x = 132x - 40
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