For Exercises 69–84, draw a graph to match the description given. Answers will vary.
has a positive derivative over
and a negative derivative over
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- In the section opener, we saw that 80x – 8000 f(x) 30 s xs 100 110 models the government tax revenue, f(x), in tens of billions of dollars, as a function of the tax rate percentage, x. Use this function to solve Exercises 55–58. Round to the nearest ten billion dollars. 55. Find and interpret f(30). Identify the solution as a point on the graph of the function in Figure 6.4 on page 439. 56. Find and interpret f(70). Identify the solution as a point on the graph of the function in Figure 6.4 on page 439. 57. Rewrite the function by using long division to perform (80x - 8000) - (x - 110). Then use this new form of the function to find f(30). Do you obtain the same answer as you did in Exercise 55? Which form of the function do you find easier to use? 58. Rewrite the function by using long division to perform (80x – 8000) - (x – 110).arrow_forwardIn Exercises 7–12, describe the relationship between the two quantities.arrow_forwardFor Exercises 111–114, use the relationship given in the right triangle and the inverse sine, cosine, and tangent functions to write θ as a function of x in three different ways. It is not necessary to rationalize the denominator.arrow_forward
- In Exercises 1–6, solve for x.arrow_forwardFor each of the equations in Exercises 59–62, y is defined as an implicit function of x. Solve for y, and use what you find to sketch a graph of the equation. 59. x² + y = 9 60. (x– 1)2 + (y + 2)² = 4 61. x? – 3y? = 16 62. 4y? — х? + 25 3 0arrow_forwardThe following graph shows a rough approximation of historical and projected median home prices for a country for the period 2000–2024. Here, t is time in years since the start of 2000, and C(t) is the median home price in thousands of dollars. The locations of stationary points and points of inflection are indicated on the graph. Analyze the graph's important features, and interpret each feature in terms of the median home price. The median home price was $_________ thousand at the start of 2000 (t = 0). The median home price has two low points; first in the year_______ and again in the year___________ when it stood at $________ thousand; The median home price peaked at the start of the year__________ at $_________ thousand. The median home price was decreasing most rapidly at the start of the year__________ when it was $___________ thousand, and increasing most rapidly at the start of the year__________ when it was $_________ thousand. Assuming that the trend shown in…arrow_forward
- America is getting older. The graph shows the projected elderly U.S. population for ages 65–84 and for ages 85 and older.The formula E = 5.8√x + 56.4 models the projected number of elderly Americans ages 65–84, E, in millions, x years after 2020.a. Use the formula to find the projected increase in the number of Americans ages 65–84, in millions, from 2030 to 2060. Express this difference in simplified radicalform.b. Use a calculator and write your answer in part (a) to the nearest tenth. Does this rounded decimal overestimate or underestimate the difference in the projected data shown by the bar graph ? By how much?arrow_forwardYour cardiac index is your heart's output, in liters of blood per minute, divided by your body's surface area, in square meters. The cardiac index, C(x), can be modeled by 7.644 C(x) = 10 s xs 80, where x is an individual's age, in years. The graph of the function is shown. Use the function to solve Exercises 95–96. 7.644 C(x) = %3D 10 20 30 40 50 60 70 80 90 Age 95. a. Find the cardiac index of a 32-year-old. Express the denominator in simplified radical form and reduce the fraction. b. Use the form of the answer in part (a) and a calculator to express the cardiac index to the nearest hundredth. Identify your solution as a point on the graph. 96. a. Find the cardiac index of an 80-year-old. Express the denominator in simplified radical form and reduce the fraction. Cardiac Index liters per minute squar e met ers 654 32arrow_forwardThe average amount A (in pounds per person) of fish and shellfish consumed in the UnitedStates during the period 1992–2001 can be modeled by A = (3.2x + 260)/(52x + 3800) where x is the number of years since 1992.Rewrite the model so that it has only whole number coefficients. Then simplify the model.arrow_forward
- In Exercises 33–38, a. Use the Leading Coefficient Test to determine the graph's end behavior. b. Determine whether the graph has y-axis symmetry, origin symmetry, or neither. c. Graph the function. 33. f(x) = x' – x² – 9x + 9 35. f(x) = 2r + 3x² – &r – 12 34. f(x) = 4x – x 36. f(x) = -r* + 25x? 37. f(x) = -x* + 6x³ – 9x² 38. f(x) = 3xª – 15x %3Darrow_forwardThe U.S. Department of Health and Human Services provides a summary of the number and rate of abortions for the period 1990–2006. Based on these data, the United States abortion rate (number of abortions per 1000 women) can be estimated by the linear function R(x) = −0.58x + 23.9 where x is the year since 1990 and R(x) is the abortion rate. (a) Based on this function, is the rate increasing or decreasing? The slope is , so the rate is . (b) Find the estimated abortion rate for 2007 and for 2017. 2007 abortions per 1000 women 2017 abortions per 1000 women (c) Estimate the year when the abortion rate will be 10. (Round your answer to the nearest year.)arrow_forwardFor Exercises 75–84, determine the r- and y-intercepts for the given function. (See Example 7) 75. f(x) = 2x – 4 76. g(x) = 3x – 12 77. h(x) = |x| – 8 78. k(x) = -|x| + 2 79. p(x) = -x + 12 80. q(x) = - 8 81. r(x) = |x – 8| 82. s(x) = |x + 3| 83. f(x) = Vx – 2 84. g(x) = – Vx + 3arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage