Television Advertising (Compare Exercises 53.) The cost, in thousands of dollars, of a 30-second television ad during the Super Bowl in the years 1980–2010 can be approximated by the following
a. Is C a continuous function of t? Why? [HINT: See Example 4 of Section 10.3]
b. Is C a
[HINT: See the “Before we go on “discussion after Example 5]
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Applied Calculus
- World Population A low-projection scenario of worldpopulation for the years 1995–2150 by the UnitedNations is given by the function y = -0.36x2 +38.52x + 5822.86, where x is the number of yearsafter 1990 and the world population is measured inmillions of people.a. Graph this function for x = 0 to x = 120.b. What would the world population have been in2010 if the projections made using this model hadbeen accurate?arrow_forwardExercises 31–38: Determine if f is a linear or nonlinear function. If f is a linear function, determine if f is a constant function. Support your answer by graphing f. -2 35. f (x) = |x + 1|arrow_forwardWorld Military Expenditure The following chart shows total military and arms trade expenditure from 2011–2020 (t = 1 represents 2011). †A bar graph titled "World military expenditure" has a horizontal t-axis labeled "Year since 2010" and a vertical axis labeled "$ (billions)". The bar graph has 10 bars. Each bar is associated with a label and an approximate value as listed below. 1: 1,800 billion dollars 2: 1,775 billion dollars 3: 1,750 billion dollars 4: 1,730 billion dollars 5: 1,760 billion dollars 6: 1,760 billion dollars 7: 1,850 billion dollars 8: 1,900 billion dollars 9: 1,950 billion dollars 10: 1,980 billion dollars (a) If you want to model the expenditure figures with a function of the form f(t) = at2 + bt + c, would you expect the coefficient a to be positive or negative? Why? HINT [See "Features of a Parabola" in this section.] We would expect the coefficient to be positive because the curve is concave up. We would expect the coefficient to be negative because the…arrow_forward
- Use this information to solve Exercises 9–11:A company is planning to produce and sell a new line of computers. The fixed cost will be $360,000 and it will cost $850 to produce each computer. Each computer will be sold for $1150. 9. Write the cost function, C, of producing x computers. 10. Write the revenue function, R, from the sale of x computers. 11. Determine the break-even point. Describe what this means.arrow_forwardSection 2.4: Chain Rule In Exercises 9–34, find the derivative of the function.arrow_forwardRetail Sales November and December retail sales,excluding autos, for the years 2001–2010 can be modeled by the function S(x) = -1.751x2 + 38.167x +388.997 billion dollars, where x is the number ofyears after 2000.a. Graph the function for values of x representing2001–2010.b. During what years does the model estimate thesales to be $550 billion?c. The recession in 2008 caused retail sales to drop.Does the model agree with the facts; that is, doesit indicate that a maximum occurred in 2008?arrow_forward
- Cell Phones Using the CTIA Wireless Survey for1985–2009, the number of U.S. cell phone subscribers (in millions) can be modeled byy = 0.632x2 - 2.651x + 1.209where x is the number of years after 1985.a. Graphically find when the number of U.S.subscribers was 301,617,000.b. When does the model estimate that the number ofU.S. subscribers would reach 359,515,000?c. What does the answer to (b) tell about this model?arrow_forward. Gold Prices The price of an ounce of gold in U.S. dollars for the years 1997–2011 can be modeled by thefunction G(x) = 11.532x2 - 259.978x + 1666.555,where x is the number of years after 1990.a. Graph this function for values of x representing1997–2011.b. According to the model, what will the price ofgold be in 2020?c. Use graphical or numerical methods to estimatewhen the price of gold will reach $2702.80per ounce.arrow_forwardU.S. Population The number of White non-Hispanicindividuals in the U.S. civilian non-institutional population 16 years and older was 153.1 million in 2000and is projected to be 169.4 million in 2050.(Source: U.S. Census Bureau)a. Find the average annual rate of change in population during the period 2000–2050, with the appropriate units.b. Use the slope from part (a) and the population in2000 to write the equation of the line associatedwith 2000 and 2050.c. What does this model project the population to bein 2020?arrow_forward
- Insurance Rates The following table gives themonthly insurance rates for a $100,000 life insurancepolicy for smokers 35–50 years of age.a. Create a scatter plot for the data.b. Does it appear that a quadratic function can beused to model the data? If so, find the best-fittingquadratic model.c. Find the power model that is the best fit for the data.d. Compare the two models by graphing each modelon the same axes with the data points. Whichmodel appears to be the better fit?arrow_forwardMarriage Rate The marriage rate per 1000 unmarried women for the years 1987–2014 is given by 132x + 1000y = 9570 where x is the number ofyears after 1980.a. Find the x-intercept of the graph of this function. b. Find and interpret the y-intercept of the graph ofthis function.c. Graph this function, using the intercepts.(Source: National Vital Statistics Report)arrow_forwardExercises 93–94: Energy The following graph shows U.S. Energy consumption. 400 350 300 250 200 150 100 50 04 1970 1990 2010 Year 93. When was energy consumption increasing? 94. When was energy consumption decreasing? Energy (millions of Btu)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage