Concept explainers
Reminder 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:
Here
a. Make a graph of
b. Calculate
c. At what population size is the growth rate the largest?
Want to see the full answer?
Check out a sample textbook solutionChapter 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. 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_forwardReminder Round all the answers to two decimal places unless otherwise indicated. Using the Quadratic Formula Solve part 1 of Example 5.14 using the quadratic formula. EXAMPLE 5.14FLIGHT OF A CANNONBALL A cannonball fired from a cannon will follow the path of the parabola that is the graph of y=y(x), where y=16(1+s2)(x/v0)2+sx feet. Here s is the slope of inclination of the cannon barrel, v0 is the initial velocity in feet per second, and the variable x is the distance downrange in feet. Suppose that a cannon is elevated with a slope of 0.5 corresponding to an angle of inclination of about 27 degrees and the cannonball is given an initial velocity of 250 feet per second. See Figure 5.62. Part 1 How far will the cannonball travel?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_forward
- 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 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_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_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 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_forwardReminder Round all answers to two decimal places unless otherwise indicated. A Dairy A dairy spends 25,000 per year to maintain its barns and equipment. It costs 2000 per year to feed and care for each dairy cow. a. Using C for the number of dairy cows and E for the total yearly expense, in dollars, find a formula that gives the total yearly expense as a linear function of the number of dairy cows. b. Use functional notation to express the total expense if the dairy has 30 cows. c. Calculate the value from part b.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 answer to two decimal places unless otherwise indicated. More on the Dairy This is a continuation of Exercise 1. The yearly income 1, in dollars, for the dairy comes from milk production, which depends on the number C of dairy cows. Each dairy cow produces 2500 gallons of milk per year, and the dairy sells milk for 2.00 per gallon. a. Find a formula that gives l as a linear function of C. b. Using the information from Exercise 1, determine the smallest number of cows the dairy needs in order to at least break even. Your answer should be a whole number. A Dairy A dairy spends 25,000 per year to maintain its barns and equipment. It costs 2000 per year to feed and care for each dairy cow. a. Using C for the number of dairy cows and E for the total yearly expense, in dollars, find formula that gives the total yearly expense as a linear function of the number of dairy cows. b. Use functional notation to express the total expense f the dairy has 30 cows. c. Calculate the value from part b.arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Gasoline Prices In 1960, the average price per gallon of gasoline was 31 cents per gallon. Form 1960 to 2000, prices increased, on average, by 2.5 cents per gallon per year. 4 a. Using G for the price, in cents per gallon, and t for the time, in years, since 1960, use a formula to express G as linear function of t. b. What price per gallon does the model yield for 1990? Note: The actual price was 1.00 per gallon. c. Use the Internet to find the average price of gasoline for the current year. Does the model from part a give a price near the current price?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning