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Reminder Round all answers to two decimal places unless otherwise indicated.
Find the quadratic determined by
11. Find the quadratic determined by
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Chapter 5 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all the answers to two decimal places unless otherwise indicated. Women Employed Outside the Home The following table shows the number, in millions, of women employed outside the home in the given year. Year Number, in millions 1942 16.11 1943 18.70 1944 19.17 1945 19.03 1946 16.78 a. Use regression to find a quadratic model for the data. Round the regression parameters to three decimal places. b. Express using functional notation the number of women working outside the home in 1947, and then estimate that value. c. The actual number of women working outside the home in 1947 was 16.90 million, whereas in 1948 the number was 17.58 million. In light of this, is a quadratic model appropriate for the period from 1942 through 1948?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Chemical Reaction The following table shows for a certain chemical reaction, the rate of reaction R, in moles per second, as a function of the concentration x, in moles per cubic meter, of the product. Concentration x 10 20 30 40 50 Reaction rate R 18 12 7 3 0 a. Use quadratic regression to find a model for the data. Round regression parameters to three decimal places. b. Use your model to estimate R(24), and explain what your answer means. c. Estimate the concentration at which the reaction rate is 6 moles per cubic meter per second. Consider concentrations only up to a level of 50moles per cubic meter.arrow_forwardReminder Round all the answers to two decimal places unless otherwise indicated. Traffic Accidents The following table shows the rate R of vehicular involvement in traffic accidents per 100,000,000 vehicle-miles as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets. Speed s Accident rate R 20 1600 25 700 30 250 35 300 40 700 45 1300 a. Use regression to find a quadratic model for the data. b. Calculate R(50) and explain what your answer means in practical terms. c. At what speed is vehicular involvement in traffic accidents for commercial vehicles driving at night on urban streets at a minimum?arrow_forward
- 5.5 EXERCISES Reminder Round all answers to two decimal places unless otherwise indicated. Estimating Wave Height Sailors use the following quadratic function to estimate wave height h, in feet, from wind speed w, in miles per hour: h=0.02w2 a. What wave height does the formula give for a wind speed of 25 miles per hour? b. A sailor observes that the wave height is 4 feet. According to the formula above, what is the speed of the wind?arrow_forwardReminder Round all the answers to two decimal places unless otherwise indicated. Vehicles parked The table shows the number, in thousands, of vehicles parked in the central business district of a certain city on a typical Friday as a function of the hour of the day. Hour of the day Vehicles parked thousands 9 A.M 6.2 11 A.M 7.5 1 P.M 7.6 3 P.M 6.6 5 P.M 3.9 a. Use regression to find a quadratic model for the data. Round the regression parameters to three decimal places. b. Express using functional notation the number of vehicles parked on a typical Friday at 2 P.M., and then estimate that value. c. At what time of day is the number of vehicles parked at its greatest?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Quadratic Formula Use the quadratic formula to solve 2x2x1=0.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Cubic Regression Use cubic regression to model the following data. x 2 1 0 1 2 y 1.4 2.7 3.0 2.9 3.0arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Falling with a Parachute If an average-sized man jumps from an airplane with a properly opening parachute, his downward velocity v=v(t), in feet per second, t seconds into the fall is given by the following table. t=Secondsintothefall v=Velocity 0 0 1 16 2 19.2 3 19.84 4 19.97 a. Explain why you expect v to have a limiting value and what this limiting value represents physically. b. Estimate the terminal velocity of the parachutist.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. A Falling Rock A rock is thrown downward, and the distance D, in feet, that it falls in t seconds is given by D=16t2+3t. Find how long it takes for the rock to fall 400 feet by using a. the quadratic formula. b. the crossing-graphs method.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Market Supply and demand The quality of wheat, in billions of bushels, that wheat suppliers are willing to produce in a year and offer for sale is called the quantity supplied and is denoted by S. The quantity supplied and is determined by the price P of wheat, in dollars per bushel, and the relation is P=2.13S0.75. The quantity of wheat, in billions of bushels, that wheat consumers are willing to purchase in a year is called the quantity demanded and is denoted by D. The quantity demanded is also determined by the price P of wheat, and the relation is P=2.650.55D. At the equilibrium price, the quality supplied and the quality demanded are the same. Find the equilibrium price for wheat.arrow_forwardReminder Round all the answers to two decimal places unless otherwise indicated. Sales Growth A class of models for population growth rates in marine fisheries assumes that the harvest from fishing is proportional to the population size One such model uses a quadratic function: G=0.3n0.2n2. Here G is the growth rate of the population, in millions of tons of fish per year, and n is the population size, in millions of tons of fish. a. Make a graph of G versus n. Include values of n up to 1.7 million tons. b. Calculate G(1.62) and explain what your answer means in practical terms. c. At what population size is the growth rate the largest?arrow_forwardReminder Round all the answers to two decimal places unless otherwise indicated. Sales Growth The rate of growth G, in thousands of dollars per year, in sales of a certain product is a function of the current sales level s, in thousands of dollars, and the model uses a quadratic function: G=1.2s0.3s2. The model is valid up to a sales level of 4 thousand dollars. a. Draw a graph of G versus s. b. Express using functional notation the rate of growth in sales at a sales level of 2260, and then estimate that value. c. At what sales level is the rate of growth in sales maximized?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt