Concept explainers
Reminder Round all the answers to two decimal places unless otherwise indicated.
Using the
EXAMPLE
A cannonball fired from a cannon will follow the path of the parabola that is the graph of
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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. 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_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 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_forwardReminder 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_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. 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
- Reminder Round all answers to two decimals places unless otherwise indicated. A Wheelchair Service Ramp The Americans with Disabilities Act ADA requires, among other things, that wheelchair service ramps have a slope not exceeding 1/12. a. Suppose the front steps of a building are 2 feet high. You want to make a ramp conforming to ADA standards that reaches from the ground to the top of the steps. How far away from the building is the base of the ramp? b. Another way to give specifications on a ramp is to give allowable inches of rise per foot of run. In these terms, how many inches of rise does the ADA requirement allow in 1 foot of run?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Walking and Running You live east of campus, and you are walking from campus toward your home at a constant speed. When you get there, you rest for 5minutes and then run back west at a rapid speed. After a few minutes, you reach your destination, and then you rest for 10minutes. Measure your location as your distance west of your home, and make graphs of your location and velocity.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. The Cannon with a Different Muzzle VelocityIf the cannonball from example 6.7 is fired with a muzzle velocity of 370feetpersecond, it will follow the graph of h=x32(x370)2, where distances are measured in feet. a.Plot the graph of the flight of the cannonball. b.Find the height of the cannonball 3000feet downrange. c.By looking at the graph of h, determine whether dhdx is positive or negative at 3000feet downrange. d.Calculate dhdx at 3000feet downrange and explain what this number means in practical terms.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning